- Bangor University

Prifysgol Bangor
Bangor University
ABA-based interventions to increase social and mathematical skills in children with
developmental disabilities in school settings
Pagona Tzanakaki
Thesis submitted to the School of Psychology, Bangor University, in partial fulfilment for the
degree of Doctor of Philosophy
October 2012
v
Acknowledgements
First of all I want to say “Thank You” to God, the Father of Jesus and my Father, for I would
have never started or completed this project without Him. You are the God of new
beginnings!
I was privileged to study under an amazing supervision team: Prof. Richard Hastings, Dr Carl
Hughes and Dr Corinna Grindle. My deepest gratitude for your guidance, patience,
encouragement, kindness and humour during the last four years.
Thank you to the Greek Ministry of Education for funding my studies.
Thank you to Susie Nash and all the other members of the IDDRG for their kindness and
support.
Thank you to Kath Huxley, Maria Saville and all the staff members of the Westwood ABA
class for helping me during my first steps with ABA.
Thanks to Jonathan Morgan, Glenda Powel and the staff of Ysgol Y Gogarth for the two
lovely years in Llandudno. Also to Denise Foran, Maggie Hoerger and Evagelia Katseli for
their support and for sharing their expertise with me.
Thanks to all the beautiful children who participated in the studies and their families; it has
been a privilege working with you all!
Thank you to my mom, for her love, support and encouragement through it all.
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Table of Contents
Declarations...................................................................................................................ii
Acknowledgements........................................................................................................v
Table of Contents...........................................................................................................vi
List of Tables and Figures..............................................................................................ix
Chapter 1: Introduction: Education of children with autism..........................................1
Summary............................................................................................................2
Interventions for children with autism...............................................................4
The behavioural model of intervention..............................................................5
School education of children with autism..........................................................7
The Westwood School ABA class.....................................................................9
Structure of thesis and background to the included studies..............................12
Chapter 2: Use of a Tactile Prompt to Increase Social Initiations in Children with
Autism...........................................................................................................................18
Abstract..............................................................................................................19
Introduction........................................................................................................20
Study 1................................................................................................................24
Method................................................................................................................24
Results.................................................................................................................33
Discussion...........................................................................................................36
Study 2................................................................................................................37
Method................................................................................................................37
Results.................................................................................................................40
General discussion..............................................................................................41
Chapter 3: Teaching Mathematics to Children with Autism: A Systematic Review ....48
Abstract..............................................................................................................49
Introduction........................................................................................................50
vii
Method................................................................................................................52
Results.................................................................................................................55
Discussion...........................................................................................................69
Chapter 4. An Individualized Curriculum to Teach Numeracy Skills to Children with Autism:
Program Description and Pilot Data...............................................................................75
Abstract..............................................................................................................76
Introduction........................................................................................................77
Method...............................................................................................................82
Results................................................................................................................92
Discussion..........................................................................................................95
Chapter 5: An Individualized Numeracy Curriculum for Children with Intellectual
Disabilities: A single blind pilot randomized controlled trial......................................101
Abstract............................................................................................................102
Introduction......................................................................................................103
Method.............................................................................................................106
Results..............................................................................................................118
Discussion........................................................................................................124
Chapter 6: General Discussion.....................................................................................129
Methodological limitations of the current research..........................................133
Implications for future research........................................................................135
Practical implications of the present research: applying acquired knowledge in the
context of a Greek special needs pre-school....................................................138
Conclusions......................................................................................................142
References....................................................................................................................143
Appendices...................................................................................................................155
1. Information to participants (Chapter 2)........................................................156
viii
2. Manual for the training phase of the tactile prompt project.........................162
3. Samples of rule cards...................................................................................186
4. Information for participants (Chapter 4)......................................................190
5. Letter to parents asking for permission for a follow-up test........................197
6. Sample lesson from the adapted Maths Recovery curriculum for children
with ASD........................................................................................................200
7. Information for participants (Chapter 5).....................................................203
8. Letter to parents asking permission for a follow-up test.............................210
9. Randomization protocol............................................................................. 214
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List of Tables and Figures
Table 3.1: Summary of studies aiming to teach mathematics to children with autism........56
Table 3.2: Summary of studies including participants without autism and/or
non- mathematical targets.........................................................................................62
Table 4.1: Participant characteristics....................................................................................84
Table 4.2: TEMA-3 test results pre-, post- Maths Recovery intervention, and follow-up...93
Table 4.3: EN - CBM test results pre- and post- Maths Recovery intervention...................95
Table 5.1: Participant characteristics..................................................................................107
Table 5.2: Number of session and total instructional time for children of the intervention
group.....................................................................................................................112
Table 5.3: Pre-, post intervention and follow-up scores for the intervention and control
groups....................................................................................................................120
Figure 2.1: Initiations to peers and peers’ responses for Alex, Peter and Reuben...............34
Figure 2.2: Initiations to peers and peers’ responses for Victor and Katie..........................42
Figure 5.1: Consort style diagram......................................................................................116
Figure 5.2: RCI results.......................................................................................................122
Chapter 1
Chapter 1: Introduction: Education of children with autism
1
Chapter 1
2
Summary
As a teacher of young children who was interested in learning how to work effectively
with children with autism, my original aim when I planned the projects that would be
included in the present thesis was to explore different areas of the education of these children
within ABA-based school environments. I had the opportunity both to work and to conduct
research in such a setting, described in this first chapter of the thesis. About halfway through
my research however, after the completion of two empirical studies, the occurrence of certain
changes of circumstances within the school setting meant that it would not be possible to
continue conducting research there as previously planned. Consequently, I had to make
adjustments to the original focus of my PhD research and plan studies that would be
conducted in different school settings that serve children with intellectual disability as well as
autism. As one of the first two studies (conducted in the ABA school setting) involved the
adaptation and initial evaluation of a numeracy curriculum for children with autism, I decided
to focus on the academic area of mathematics for the remaining projects of my PhD research.
Chapter 1 of the present thesis starts with a brief overview of autism spectrum
disorders. The issue of the various interventions implemented with children with autism is
discussed next, and the behavioural model of early intervention is described. The area of
school-based education of children with autism is discussed in the next section, followed by a
description of the ABA school setting where the first two empirical studies included in the
present thesis were conducted. In the final part of Chapter 1 an overview of the structure of
the present thesis, and a brief description of the studies presented in the following chapters
are presented.
Chapter 1
3
Just about 70 years ago the term “autism” (derived from the Greek word for “self”)
was used for the first time by Leo Kanner (1943) to describe the unusual behaviours of a
small group of children who preferred to be alone, did not show interest in other people and
exhibited peculiar interests for certain objects. Since then, the defining characteristics and
diagnostic criteria for Autism Spectrum Disorders (ASD) have been described in more detail
within diagnostic manuals (DSM-IV, APA 2000; ICD-10, World Health Organisation, 1993).
These characteristics include impairments in three major areas: (a) social interaction (e.g.,
failure to develop relationships with peers, lack of interest in shared activities, absence of
eye-contact and other non-verbal social behaviours); (b) communication (e.g., lack or delayed
development of spoken language, absence of non-verbal communicative behaviours such as
gestures, lack of initiating to others even when the person can speak) and (c) the existence of
unusual, restricted interests and stereotyped behaviours (e.g., preoccupation with certain parts
of objects instead of functional engagement, persistence in routines and difficulties with
transition and change, presence of repetitive, stereotyped movements such as rocking, handflapping, spinning objects, squinting, lining up items).
As the term “spectrum” implies, individual children who qualify for a diagnosis of
ASD present quite diverse social, communicative, and behavioural profiles (Symon &
Boettcher, 2008). For example, some children may be completely non-verbal or have some
echolalic language. Others have some verbal skills, however the quantity and the quality of
verbal interactions are limited. For example, a child may have the ability to ask for desired
items but be unable to ask questions or initiate to other children (Koegel, 2000). A number of
children exhibit disruptive behaviours such as tantrums, aggression and self-injury. Levels of
cognitive development vary as well, with an estimated 50-70% of children having an
intellectual disability while others have IQ scores that fall within the typical range (Lovaas,
2003; Matson & Shoemaker, 2009; Wing, 1993).
Chapter 1
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Interventions for Children with Autism
There are severe impairments connected with autism, considerable diversity of
individual profiles, and the number of children who are being diagnosed with ASD
worldwide is rising (Wilczynski & Christian, 2008). Therefore, there is an increasing interest
in the disorder and a large amount of related research. It is likely that autism is a result of an
atypical brain development. At this point in time, despite the progress in scientific areas such
as genetics, brain imaging and immunology, the exact aetiology of ASD is still unknown and
no evidence-based medical treatments that address the core causes of autism are available
(Rapin & Tuchman, 2008).
When a child receives an ASD diagnosis, often his/her parents are faced with
confusion regarding the next step they should take, and the choice of the most appropriate
intervention. Numerous “treatments” have been developed that could be broadly grouped into
the following categories: (a) standard therapies (e.g., speech and language therapy, music
therapy), (b) skill-based interventions (e.g., ABA-based intervention, Social Stories), (c) diets
and vitamin supplements (e.g., gluten and casein-free diets), (d) physiological treatments
(e.g., sensory integration, auditory integration training), (e) alternative treatments (e.g.
aromatherapy), (f) relationship-based treatments (e.g., gentle teaching, Son-rise), and (g)
programs that combine elements of different treatments (Green et al., 2006). However many
of these have not been evaluated using rigorous scientific methods and are based on anecdotal
evidence only (Green, 1996). In many cases professionals who deliver the child’s diagnosis
do not offer recommendations on evidence-based interventions. Therefore, parents turn to
other sources for relevant information, such as the internet or other parents of a child with
autism (Maurice, Mannion, Letso, & Perry, 2001; Tzanakaki, Grindle, Hastings, & Hughes,
2012). Often more than one intervention is tried by parents. According to an internet survey
conducted with 552 parents of children with autism, each family were using on average seven
Chapter 1
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different treatments with their child at the time of the survey (Green et al., 2006). Results
indicated that strong empirical evidence may not be the main criterion for choosing an
intervention; parents reported using both evidence-based interventions and those lacking
empirical evidence (Green et al., 2006).
The Behavioural Model of Intervention
An extensive amount of research including a number of systematic reviews and metaanalyses of the literature indicate that educational interventions based on the principles of
Applied Behaviour Analysis (ABA) are the benchmark treatments for ASD (Eikeseth, 2009;
Eldevik et al., 2009; Peters-Sheffer, Didden, Korzilius, & Sturmey, 2011; Reichow &
Wolery, 2009; Reichow, 2012). Early Intensive Behavioural Intervention (EIBI) programs
are individually designed to correspond to each child’s needs. They encompass a wide range
of skills including following instructions, verbal skills (e.g., requesting for desired items,
labelling items/actions/persons, answering questions), imitating others’ behaviour, self-help
skills, play skills, pre- academic and academic skills. Intervention implementation preferably
begins at an early age (under the age of 5). Teaching initially is conducted at the child’s home
on a one-to-one basis and is intensive (at least 20 hours per week). Program design and
supervision are undertaken by experienced persons who have extensive training in ABA
procedures. Detailed data are collected daily and decisions concerning the different areas of
the program are guided by a continuous evaluation of the data (Eldevik et al., 2009; Leaf &
McEachin, 1999; Lovaas, 2003; Maurice, Green, & Luce, 1996).
A wide range of techniques based on the principles of ABA are used within EIBI
programs. Some of the most prominent are: (a) The use of “rewards” to reinforce desired
behaviour, based on Skinner’s principle of operant conditioning (i.e., the consequences
following an instance of behaviour increase/decrease the probability of the behaviour
Chapter 1
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occurring in the future). Items or activities preferred by the student are used as reinforcers.
(b) Task analysis is used to break complicated skills into smaller, manageable steps. The
student only needs to learn one step at a time. (c) The use and systematic fading of prompts.
To teach new skills various types of prompts are often used by the teacher. Prompts range
from quite extensive (e.g., manually guiding the student to perform the task) to least intrusive
(e.g., a pointing gesture to indicate the correct answer). When the student can perform the
task with the help of the prompt, the procedure of prompt-fading (i.e., the gradual removal of
the prompt) is being implemented so that the student will eventually be able to perform the
task independently. (d) Generalisation of acquired skills. Because children with ASD may
not automatically transfer knowledge acquired in one environment to other environments, in
EIBI programs systematic steps are programmed to ensure the child can perform a task using
a variety of stimuli, with different persons presenting the instruction, and in different settings.
(e) Functional assessments of problem behaviours are conducted to identify the purpose(s)
these behaviours serve for the child. For example, a child may exhibit aggression because this
has allowed them to escape a task, ensure attention from adults, or obtain a desired item.
Identifying the function of the behaviour enables the instructors to design an appropriate
intervention (e.g. teach the child more appropriate ways of asking for a termination of a task
or a desired item, give him/her attention when the child is behaving appropriately) (Grindle,
Hastings et al., 2009; Lovaas, 2003).
Perhaps the most widely used format of one-to-one teaching within ABA programs is
discrete-trial-training (DTT) (Smith, 2001). A discrete trial is a small instructional unit that
lasts a few seconds and consists of the following parts: (a) The teacher gives an instruction to
the student; (b) the student responds (correctly or incorrectly); (c) the teacher gives a
consequence depending on the student’s response: a reward (e.g., praise, a short interval of
playing with a favourite toy) or an indication that the response was incorrect (e.g., an
Chapter 1
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informative “no”); (d) a short inter-trial interval, a pause of 2-3 seconds before the next
instruction is presented to the child. Often, immediately after the presentation of the
instruction, the teacher may assist the student to respond correctly by giving him a prompt.
School Education of Children with Autism
When children with ASD enter the school system they may be enrolled either in
general education classrooms or in classrooms serving students with special needs (whether
within a mainstream school environment or a special school). Across both of these types of
educational settings the most common model used seems to be an “eclectic” treatment that
combines elements of various interventions. Eldevik, Hastings, Jahr and Hughes (2012)
described such a model used in Norwegian pre-schools; interventions used included
alternative communication (i.e., using pictures or symbols), sensory integration (i.e.,
activities such as stretching, rocking, going on a swing, massages and listening to music), a
few ABA programs (i.e., matching, imitation), and elements of structured teaching (i.e., the
use of picture schedules, specific areas designated for work activities, tasks to be completed
placed in baskets). Hess, Morrier, Heflin and Ivey (2008) conducted a survey with teachers of
pre-school to high-school aged children with ASD in the USA. Results revealed the use of a
wide range of interventions with the five most common being gentle teaching (an
interpersonal relationship based approach), sensory integration, cognitive behavioural
modification, assistive technology and social stories. Hess et al. (2008) concluded that
evidence of effectiveness was not the primary criterion of choosing an intervention, a finding
similar to the results of the survey conducted with parents of children with ASD (Green et al.,
2006). Another important implication of the Hess et al. (2008) survey was the lack of clear
guidelines on best educational practices for children with ASD, meaning that teachers of
these children might have to make their own decisions regarding the interventions they will
use.
Chapter 1
8
As EIBI intervention usually starts before the child has reached school age, the main
body of relevant literature involves treatment conducted either at the children’s family homes
or at specialised clinics. A very small number of studies have evaluated EIBI interventions
conducted at school settings. In the study by Eldevik et al. (2012) a comprehensive (i.e.,
aiming towards the child’s overall development by targeting a wide range of areas) EIBI
model was implemented in Norwegian regular education pre-school settings with children
aged between 2 and 6 years. Each child received on average 13.6 hours of individualized
intervention per week for approximately two years. Members of the pre-school staff who
were trained and supervised by experienced behaviour analysts implemented the intervention.
Pre- and post- intervention assessments using standardized measures indicated that the
children made significant improvements on intellectual functioning (IQ) and adaptive
behaviour performance. A second group of children with similar characteristics at intake who
received treatment in pre-school settings that used the “eclectic” model of intervention
(combination of elements of various approaches) did not make any gains at the end of the
two-year period.
Another study reported the progress of six children with ASD aged between 3 and 6
years, who received intensive individualized intervention in an EIBI pre-school setting in
Ireland (McGarrel, Healy, Leader, O'Connor, & Kenny, 2009). After 3 to 4 years of
comprehensive intervention in this setting all six children made gains in IQ and adaptive
behavioural scores. Additionally, during the course of the intervention the amount of time
each child spent in individualised teaching was gradually decreased so that all 6 children
were able to attend regular education elementary classrooms on leaving the ABA pre- school
setting.
Two more studies conducted in Norway examined the effects of school-based
comprehensive EIBI on a group of 4 to 7 year old children enrolled in regular education
Chapter 1
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classrooms and compared their progress to a similar group o f children who received eclectic
treatment (Eikeseth, Smith, Jahr, & Eldevik, 2002, 2007). Children in both groups received
intervention for approximately 32 months. While attending pre-school the children (of both
groups) received on average 28 hours of individualized teaching per week; upon entrance into
elementary school individualized weekly intervention was reduced to approximately 17
hours. Results indicated that children of the EIBI group made larger gains on IQ and adaptive
behaviour measures and exhibited less severe challenging behaviours than the children of the
eclectic treatment group at post- treatment (Eikeseth et al., 2007).
Finally, another study (also conducted in Norway) experimented with a less intensive
intervention in school settings. Children of both the behavioural and the eclectic treatment
groups received 12 hours of intervention per week. Results were in favour of the behavioural
group but gains were modest compared to those attained by more intensive programs
(Eldevik, Eikeseth, Jahr, & Smith, 2006).
These findings, although still of a small scale, suggest that the ABA-based model of
comprehensive intervention for children with ASD can be successfully implemented within
school settings and that it may yield favourable results compared to the widely used eclectic
model of education.
The Westwood School ABA Class
In the UK a very small number of students with ASD receive school instruction based
on an ABA model. A recent census (Griffith, Fletcher, & Hastings, 2012) identified 14 ABA
school settings, serving 258 students with ASD aged between 3 and 17 years. These included
10 ABA schools, two ABA classes within special school settings, and another two ABA
classes within regular education school settings. One of the latter settings was situated in
North Wales. The local educational authorities of two counties in collaboration with Bangor
Chapter 1
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University established an ABA class within a local primary school, Westwood School. The
educational model is described in detail in two papers by Grindle et al. (2009; 2012); a brief
description is provided here.
A university employed ABA consultant with a doctoral degree and a long experience
in working with children with ASD was in charge of organizing the children’s individualised
teaching programs and the ongoing staff training in the class. The class served children
whose age ranged between 3 years 6 months and 7 years old. To be enrolled in the ABA class
a child had to have a diagnosis of autism, a statement of special educational needs and a
recommendation for placement within an appropriately resourced class setting by their local
educational authority. Upon enrolment in the ABA class each child’s skill level was assessed
using the ABLLS (Partington & Sundberg, 2006), an assessment tool that covers a wide
range of skills (e.g., language, play skills, self-help, social skills, pre- academic and academic
skills, motor skills). Based on the child’s baseline performance, an individualised
comprehensive curriculum (i.e., including targets from all these areas) based on widely used
published manuals for children with ASD (e.g., Leaf & McEachin, 1999; Lovaas, 2003;
Maurice et al., 1996; Partington & Sundberg, 2006) was designed by the consultant of the
class. Initial targets often included mainly “learning to learn” skills, such as being able to sit
on a chair and engage in an activity for a few seconds, following simple instructions and
appropriately communicating basic needs. For the larger part of the school day the child
worked on these targets on a one-to-one basis with ABA-trained therapists. DTT was the
teaching format used during the individualized sessions. Typically during the day each child
had sessions with two different therapists to ensure that skills would be generalized across
different instructors. Each child had his/her own work area within the ABA class consisting
of a table and chairs, drawers and shelves for teaching materials and favourite toys the child
Chapter 1
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could engage with during short breaks between tasks. Interspersed throughout the day were
small-group activities, such as assembly and singing/story time.
Integration of the children with ASD into the regular education classroom with
typically developing peers was an important target of the ABA class. Therefore as soon as the
child had acquired some basic skills he/she started spending daily some time in that setting
(within the same school) supported by an ABA therapist. Individual targets in this area
differed and were dependent on the child’s ability to adjust to the regular education class
environment and benefit from it (e.g., work on similar academic targets as typically
developing peers, follow group instructions). Some of the children were able to gradually
increase the time they spent in this environment to a few hours every day, and were thus
prepared to be enrolled in more typical school settings upon leaving the ABA class.
Outcomes of the children who attended the ABA Westwood class were recently
reported by Grindle et al. (2012). Standardized tests measuring intellectual functioning (IQ)
(Leiter - R, Roid & Miller, 1997; or Stanford-Binet Intelligence Scale - 4th edition,
Thorndike, Hagen, & Sattler, 1986), adaptive behaviours (VABS, Sparrow, Cicchetti, &
Balla, 2005) and basic language and learning skills (ABLLS-R, Partington & Sundberg,
2006) were conducted with each child at three points: at the time of enrolment, after 1 year
and after 2 years in the ABA class. Results indicated that at the end of their first year in the
class the children made marginally significant improvements on IQ scores, and significant
gains on adaptive behaviours and the different skill areas measured by the ABLLS-R. At the
end of their second year the children had continued to increase their scores and made
significant improvements on the VABS and the ABLLS-R while IQ gains were not
statistically significant. Additionally, score changes on IQ and the VABS after two years in
the ABA class were compared to those of a similar group of children who had received two
years of eclectic school intervention. According to this analysis, the children enrolled in the
Chapter 1
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Westwood class made larger improvements in both areas. There was a significant betweengroups difference on the VABS whereas the difference on the IQ scores was not significant
(Grindle et al., 2012).
Structure of Thesis and Background to the Included Studies
I am a Greek pre-school teacher with a background in regular education. Within the
Greek educational system children can be enrolled into pre-schools when they are 4 years
old, up to the age of 6 when they enter elementary school. After about 10 years of working in
regular education pre-schools I decided to explore the area of autism and took a one-year MA
course on this subject in the UK. Learning about the deficits in the three major areas of
communication, social interaction and restricted interests/ unusual behaviours was
enlightening but at the same time resulted in a number of new questions regarding how best
to teach young children who are diagnosed with ASD. According to almost every book I read
on the subject, many of which had been written by parents of children with ASD living in the
USA, ABA was recommended as an effective practice that helped the children start to learn
and progress. During the time of the MA course however, I did not have the opportunity to
observe ABA-based intervention used within the public schools I visited in the UK as the
regular practice was the eclectic model described earlier in this chapter. The only contact I
was able to have with ABA during that period was a brief visit to a London ABA school for
children with ASD.
At the end of the MA course I decided that I needed to learn more about best teaching
methodologies for children with autism before I was ready to return to Greece to work with
these children. I found that Bangor University was one of the few UK universities that
conducted research on ABA in the education of children with ASD and also had an MSc
ABA course. I was enrolled in the university for a doctoral degree that would enable me
Chapter 1
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attain the following goals: (a) gain understanding of the basic principles of ABA by
completing relevant modules, (b) have the opportunity to gain practical experience by
working in an ABA setting for children with autism, and (c) conduct research on different
aspects of the education of children with autism using effective practices under the guidance
of persons with a long experience in this field.
During the first two years of my doctoral degree I had the opportunity to work as an
one-to-one therapist for children with autism in the ABA Westwood class, first on a
voluntary basis and then as a part-time staff member. The collaborative management of the
ABA class with the local educational authorities gave Bangor University personnel and
research students the opportunity to conduct research in an environment that was organised
and managed to a very high standard by Dr Grindle, one of my supervisors, together with a
team of experienced staff. During the second year of this period the studies described in
Chapters 2 and 4 of the present thesis were conducted.
These studies were a result of my research interest in exploring new approaches in
different applied areas of ABA-based intervention for children with ASD. With the main
body of literature being focused on comprehensive educational programs that target the
child’s global development and using outcome measures of intellectual functioning (IQ) and
adaptive behaviours, other areas such as best methods to teach different curriculum domains
to children with autism have received less attention. Information on how to teach reading or
mathematics within ABA programs, for example, is limited. Similarly within existing ABA
curriculum guides (Leaf & McEachin, 1999; Maurice et al., 1996; Partington & Sundberg,
2006) the sections devoted to specific academic areas are rather concise. My aim was to
provide some new insights and evidence in various educational curriculum areas for children
with autism, using behavioural intervention methods.
Chapter 1
14
In Chapter 2 of the thesis an intervention aiming to increase social skills in children
with autism by teaching them to initiate more often to their peers is described. The method
explored involved the use of a tactile prompt, a small device like a pager that was placed in
the child’s pocket and was programmed to vibrate at regular intervals. The child was taught
to verbally initiate to a peer when he felt the vibration. Two studies comprise this chapter, the
first of which was conducted in the ABA Westwood class. The second study that aimed to
replicate and extend the findings of the first was conducted during the following academic
year in different school settings, under joint supervision of Dr Grindle and myself. Both
studies found that the intervention was effective as the rate of the target children’s initiations
towards their peers increased. Additionally, in the second study, the use of the tactile prompt
was successfully faded while the rate of initiations remained high.
The remaining three main chapters of the present thesis focus on a different
curriculum area, that of mathematical interventions. An initial question explored in this part
of the thesis involves mathematical interventions that have been used with children diagnosed
with autism in published research. An exploratory search into the literature of interventions
for children with autism revealed that a small number of studies have described mathematical
interventions with these children. Some of these studies have been included in meta-analyses
on teaching mathematics to students with intellectual disabilities (e.g., Browder, Spooner,
Ahlgrim-Delzell, Harris, & Wakeman, 2008; Buttler, Miller, Lee, & Pierce, 2001). However
no systematic reviews or meta-analyses that have focused specifically on children with
autism were found. Therefore a systematic review of the literature was conducted, presented
in Chapter 3 of this thesis.
An exploratory mathematical intervention with children with autism is described in
Chapter 4 of the present thesis. Because of the small number of lessons and the lack of
detailed guidance on teaching mathematics within ABA curriculum guides, the possibility of
Chapter 1
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using a detailed numeracy curriculum that was initially designed for use with typically
developing children who have mathematical difficulties was explored. The Maths Recovery
curriculum was adapted for use with children with autism in ABA intervention programs. The
adapted numeracy program was then used to teach all the children in the ABA Westwood
class who had the necessary pre- requisite skills and whose numeracy skills fell below their
age level (all but two of the children enrolled in the class at that point). Results from this
practice-focused research evaluation indicated that all the children who participated in the
study improved their numeracy skills.
The two research studies described in Chapters 2 and 4 were conducted during the last
year of the collaboration between Bangor University and the local educational authorities for
the management of the ABA class, with some of the same children whose progress was
documented by Grindle et al. (2012). The fact that the university would not be involved any
more in the management of the ABA class meant that university personnel and students
would not be able to continue conducting research in this venue. Consequently, a revision of
the focus of my PhD research became necessary at that point. Following the adaptation of the
Maths Recovery curriculum described in Chapter 4, I decided that teaching mathematics to
children with autism and other developmental disabilities was an area I would like to further
explore. The small scale evaluation of the adapted Maths Recovery curriculum provided
some initial evidence on the effectiveness of this numeracy program with children with
developmental disabilities. To help us design further evaluation steps, the framework
suggested by the Medical Research Council (MRC, 2008) on the development and evaluation
of complex interventions was considered. According to the MRC guidelines recommended
stages in this process include the identification/development of a theory, followed by a series
of pilot studies that test different aspects of feasibility; the complex intervention is then
evaluated, first at an exploratory and then at a more definite level, preferably using
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randomized controlled trial (RCT) studies. Finally the intervention can be disseminated into
non-research environments.
In the pilot study described in Chapter 4 a number of elements of the implementation
of Maths Recovery with children with ASD were tested; we found that within an ABA school
environment the teaching manual and the procedures for staff training and supervision
enabled the therapists to effectively implement the intervention; the DTT teaching format was
compatible with the individualized teaching model of Maths Recover; finally, the outcome
measures (especially TEMA-3) depicted the post-intervention progress of the children. A
next possible stage could involve a study that would evaluate the program with a large
number of participants, using a strong methodological design (such as an RCT study). An
additional research question involved the possibility of implementing this intervention in a
non-ABA school setting (e.g. a special needs school). Before a definitive RCT study could be
conducted in such an environment the following additional elements needed to be tested for
feasibility: (a) the willingness of parents to allow their children to be randomly allocated into
an intervention and a control group; (b) the delivery of an individualised intervention within a
less resourced school environment (i.e., a lower staff-to-students ratio, lack of staff expertise
on ABA teaching methods); (c) the effort required for training and supervision of staff within
that environment; and (d) the resources needed to teach a larger number of children.
Conducting a pilot RCT study that would help us test these elements was therefore
considered as a next appropriate step.
Dissemination of the positive results of the different university led ABA intervention
projects for children with autism created an interest for the application of similar research
projects among local special needs schools in North Wales. One of these schools, serving
children with intellectual and developmental disabilities, invited research teams from Bangor
University to cooperate with school personnel on the areas of managing challenging
Chapter 1
17
behaviours, early comprehensive intervention of young children with autism, and teaching of
academics (reading and mathematics). The possibility of conducting an RCT study using the
adapted Maths Recovery curriculum was discussed with the head teacher of the school; both
he and the children’s parents agreed that we could conduct a randomized controlled study
with a waiting list control design, so that the children in the control group could also receive
the intervention at a later point. This study is described in Chapter 5 of the present thesis.
Results indicated that the adapted Maths Recovery curriculum was successfully implemented
and resulted in increased numeracy scores for the children of the intervention group.
Finally, Chapter 6 of the present thesis contains a general discussion on the different
themes arising from the previous chapters. Then the methodological limitations of the
empirical studies are discussed as well as implications for future research. Also, I present
some initial information on how the knowledge acquired during my doctoral studies can be
applied in the context of the Greek educational system where I have started work in a special
needs pre- school setting that serves children with intellectual and developmental disabilities.
Chapter 2
18
Chapter 2. Use of a Tactile Prompt to Increase Social Initiations in Children with Autism1
1
I want to thank the following persons who contributed to this empirical study and who will be at times
referred to as co-authors of this chapter: Corinna Grindle, Sarah Dungait, Amy Hulson-Jones, Maria Saville, Carl
Hughes and Richard Hastings.
Chapter 2
19
Abstract
Making appropriate verbal initiations to others is an aspect of social interactions that seems to
be especially problematic for individuals with autism. A variety of teaching and prompting
methods have been developed to address the issue. A method that has been reported to be
effective in the literature involves the use of a tactile prompt, a small device that can fit in the
participant’s pocket and can be programmed to vibrate at regular intervals. The aim of the
current project was to extend the existing research on the use of the tactile prompt by
incorporating reinforcement during intervention and attempting a systematic fading of the
prompt. The project consists of two similar studies. Three children with autism participated in
Study 1and two children in Study 2. In both studies the intervention was conducted during
free-play activities with mainstream peers. Results indicated that the participants’ verbal
initiations to their peers increased in comparison to baseline. Additionally, in Study 2 the use
of both the tactile prompt and the prosthetic reinforcement were successfully faded.
Implications regarding the use of covert prompting methods to help individuals with autism
in the area of social interactions are being discussed.
Chapter 2
20
One of the core deficits, and a diagnostic criterion for autism, is difficulties in the area
of social interaction. More specifically, persons with autism may have impairments in the use
of non-verbal behaviours (such as eye-contact and body posture), fail to develop typical
relationships with peers, and participate in a limited way in reciprocal activities such as
games (American Psychiatric Association, 2000). Even after language improvements have
been achieved through intervention, social difficulties often continue to persist presenting
challenges to professionals who work with individuals with autism (Weiss & Harris, 2001).
Initiating towards peers is one aspect of social interaction that seems to be especially
problematic for young children with autism (Hauk, Fein, Waterhouse, & Feinstein, 1995).
Data on the rate of verbal initiations that typically developing children emit towards their
peers indicate that child characteristics and environmental variables result in variability
among children (Greenwood, Walker, & Todd, 1981; Tremblay, Strain, Hendrickson, &
Shores, 1981). A few researchers have suggested that on average, 3- to 6-year old typically
developing children emit one initiation every two minutes during unstructured play situations
(McGrath, Bosch, Sullivan, & Fuqua, 2003; Zanolli, Dagget, & Adams, 1996). Children with
autism might initiate towards adults, but rarely spontaneously seek to interact with their peers
(Koegel, Koegel, & McNerney, 2001; Oke & Schreibman, 1990). Therefore, conversations
and interactive play between children with autism and other children are limited, resulting in
reduced social and verbal learning opportunities (Koegel, Koegel, Shoshan, & McNerney,
1999b; Nikopoulos & Keenan, 2003). Furthermore, research comparing initiations of children
with autism and those with intellectual disability shows that both the quantity and quality of
initiations towards peers is lower for children with autism. In terms of quality, when
initiations occur, they are of a lower developmental level (Hauk et al., 1995).
There is some evidence that social initiations might be a pivotal behaviour (or pivotal
response class) for children with autism, which if successfully increased might result in
Chapter 2
21
improvements in the child’s overall development (Koegel & Koegel, 2006). For example, the
presence of a higher level of spontaneous initiations at pre-intervention correlated with better
post-intervention outcomes for children receiving early behavioural intervention (Koegel et
al., 1999b). In a second phase of the Koegel et al.(1999b) study, the authors systematically
incorporated verbal initiations targets (first toward adults, and later extending to peers) in the
intervention programs of four children with autism who lacked this skill. Initially the children
were taught to ask an adult “what’s that?” in the presence of a semi-concealed highly
preferred item. Subsequent targets included initiations such as: “where is it?” and “whose is
it?” involving items; “what is happening?” involving story books; and “play slide” towards a
peer at the playground. Two 1-hour sessions were conducted weekly. After two and a half
years of intervention, the four participants’ verbal initiations showed marked improvement.
The children also scored at an age-appropriate level in their pragmatic language skills,
adaptive behaviour scores and social and community functioning (Koegel et al., 1999b).
These findings suggest that incorporating social initiation training within early intervention
programs might enhance overall effectiveness.
Previous behaviour analytic studies have explored a number of procedures to help
increase the rate of social initiations in children with autism. Swaggart et al. (1995) used a
social story combined with verbal prompting and reinforcement procedures to teach a girl
with autism to greet her peers. A script and script-fading procedure was used in another
project involving four children with autism (Krantz & McClannahan, 1993). Following this
intervention, all children reached a similar level of initiations as their typically developing
peers. Video modelling was employed in a study by Nikopoulos and Keenan (2007) who
taught four children with autism to initiate towards an adult. These authors found that the
newly acquired behaviour generalized towards a peer without further training. However, the
generalization sessions were conducted in the same experimental setting as the previous
Chapter 2
22
sessions with the adult. No generalization check was conducted in a more naturalistic
environment, such as the children’s classroom or the playground.
Each of these existing studies incorporated the use of a prompting method to help the
child initiate towards others. Prompts are defined as antecedent stimuli which can have a
variety of forms (modelling, verbal, gestural, etc.) that cue the learner to emit the desired
behaviour (Cooper, Heron, & Heward, 2007). Prompting methods have been widely and
effectively used within Applied Behaviour Analysis (ABA) interventions when social skills
are being targeted. However, a number of limitations relating to prompts being used in
mainstream inclusive practice settings need to be considered. For example, overt prompts can
be distracting for the child and for others in the environment and perhaps disrupt the flow of
interactions. Overt prompts might also draw attention to the child’s difficulties and thus make
him appear as “different” from others (Anson, Todd, & Cassaretto, 2008). Another problem
that often arises is that when the prompts are faded, the acquired behaviour may not be
maintained (Odom, Hoyson, Jamieson, & Strain, 1985).
A prompting method that has shown some promise in helping children with autism
emit verbal initiations towards their peers is the use of a tactile prompt. A tactile prompting
device is a pocket sized vibrating pager that is either activated through a transmitter by a
trainer or is programmed to vibrate at regular intervals. The individual is taught to associate
the prompt with a specific behaviour. At the intervention stage, the teacher can activate the
device to prompt the target person to engage in the desired behaviour. An important
advantage of the method is that it is unobtrusive and covert. People other than the target
person need not be aware that he/she is being prompted. Another consideration is that tactile
prompts might be easier to fade compared to other prompting methods, such as verbal
prompts.
Chapter 2
23
A small number of studies have found the tactile prompt to be effective in teaching a
variety of skills to young people with autism. Anglesea, Hoch, and Taylor (2008) taught three
teenagers with autism to eat at a slower pace. A device programmed to vibrate at variable
intervals (range 10 – 30 seconds) prompted them to take a bite at each vibration. Food
consumption pace decreased for all three participants. Safety skills were targeted in a study
by Taylor, Hughes, Richard, Hoch and Rodriquez Coello, (2004) who successfully taught
three teenagers to seek assistance when lost in a community setting. At the vibration of the
device (activated by a trainer invisible to the student with autism), the participant approached
the nearest adult and indicated he needed assistance by handing him/her a communication
card. Anson, Todd and Cassaretto (2008) used a tactile prompt to cue students with autism
who attended a mainstream classroom to exhibit “on-task” behaviour (e.g. pay attention to
the teacher or engage in appropriate activities). They compared this prompting method to
verbal and gestural prompting and found that the covert, non-intrusive tactile prompt was at
least as effective as the more traditional prompting methods.
We also found two existing studies in which a tactile prompting device was used to
help children with autism make verbal initiations. Taylor and Levin (1998) used a device that
could be programmed to vibrate at regular intervals to increase the spontaneous initiations of
a nine-year-old child, Ron. During indoor play activities, Ron was taught to initiate to an
adult using phrases such as “Mary, I am making a tiger!” Results indicated that Ron emitted
between 8 and 10 verbal initiations per 10-minute session during the tactile prompt condition.
Follow-up probes with typically developing peers showed that Ron emitted a high rate of
initiations when the tactile prompt was activated. However, when the device was inactive in
his pocket he made very few initiations. Shabani et al. (2002) used a device that was activated
by a remote control and replicated Taylor and Levins’ study with three children with autism.
Children were taught to initiate to typically developing peers using the phrases: “Look at
Chapter 2
24
this”, “I have...” (toy label), and “Do you want to play?” during free-play activities. Data on a
second untrained behaviour - verbal responses to peers’ initiations - were also collected. The
authors found that the use of the tactile prompt resulted in increased initiations and responses.
Fading of the tactile prompt by reducing the frequency of vibrations was attempted with two
of the three children. This phase was partially successful with one child but the other child
had a significant decrease of initiations during the fading procedure.
Existing research provides some evidence that the tactile prompt can be effective in
increasing verbal initiations for children with autism. However, a significant question that has
not yet been answered is whether it is possible to fade the tactile prompt while maintaining
the increased levels of verbal initiations. A hypothesis that has not yet been tested is whether
incorporating prosthetic reinforcement during the tactile prompt intervention might result in a
more successful fading procedure. Reinforcement was not used by Taylor and Levin (1998)
and was only used during the training phase in the Shabani et al. (2002) study. Accordingly,
the present project comprised of two studies aimed to replicate and extend the existing
research on the subject by: (a) incorporating the use of reinforcement during the intervention
phase, and (b) attempting fading of both the tactile prompt and the prosthetic reinforcement.
Study 1
Method
Participants
Three boys diagnosed with autism participated in the study. All were attending an
autism unit attached to a mainstream elementary school in North Wales, UK. Children
enrolled in the unit received ABA based individualized intervention (see Grindle et al. 2009;
2012). As part of the ongoing annual assessments administered to all the students in the unit,
Chapter 2
25
the three participants were assessed for IQ and adaptive behaviour scores. The tests were
conducted towards the end of the intervention period independently of the present study.
Alex was 7 years, 3 months old. At the time of the study he spent a large proportion of
his school day in the mainstream classroom accompanied by an ABA-trained therapist. He
could talk in full sentences. He enjoyed participating in play activities with his mainstream
peers. However, he rarely initiated verbally towards his peers. His IQ score on the Stanford–
Binet Intelligence Scale–Fourth Edition (SB-IV, Thorndike et al., 1986) was 93. On the
Vineland Adaptive Behavior Scale–Survey Form (VABS, Sparrow et al., 2005) he had a
composite score of 79, communication 86, and socialization 80.
Peter was 6 years, 2 months old. He had good language skills and would often
approach adults and verbally initiate. However, he had a low level of interactions with other
children and he generally chose to play by himself. During playtime, he would sometimes say
a phrase related to a favourite cartoon story (e.g. “I’m Jono the dog!”), without directing this
to another individual. Peter had an IQ score of 102 on the SB-IV and his composite score on
the VABS was 79, while his scores on the communication and the socialization domains were
93 and 77 respectively.
Reuben was 4 years, 6 months old. He could talk in sentences consisting of up to three
words. During playtime, he would engage in parallel play alongside other children but did not
interact with them. Reuben had an IQ score of 83 on the SB-IV. His adaptive skills standard
scores on the VABS were: composite 68, communication 74, and socialization 68.
Settings
Based on each child’s individualized program in the unit, an intervention setting was
chosen that would offer the most opportunities for interactions with peers. An additional goal
Chapter 2
26
was to implement the intervention in a setting with mainstream peers rather than other
children with autism so that any initiations the participants made would have more
possibilities of being reciprocated. Alex spent most of his daily free-play time in the large
play yard of the mainstream school with typically developing peers. Therefore, this setting
was chosen for him. Football games were often played in this yard, an activity Alex enjoyed.
There were also markings on the ground for playing hopscotch and jumping circles. An
indoor setting was chosen for Reuben who spent about half an hour daily in a free-play area
of the pre-kindergarten with typically developing children who were approximately a year
younger than him (3-year-olds). Toys in this setting included building blocks, cars, trains and
a doll’s house. There were also a few tables used for activities such as drawing, painting or
play-dough. Peter did not spend time in mainstream school at the time of the study because
he exhibited high levels of anxiety in that setting. Consequently, we could not implement the
intervention in a free-play setting with mainstream peers. Instead, we used the small play
yard that children of the autism unit shared with children from the mainstream kindergarten
class. Subsequently, Peter had opportunities to initiate towards both children with autism and
typically developing children. There was a slide in this play yard and a variety of outdoor
toys such as bikes, water play materials, strollers and dolls.
The training phase with each of the children (see Procedure) was conducted at their
individualised teaching area within the ABA unit. This was divided from the rest of the
classroom by a screen and was equipped with a table and small chairs, a set of drawers for
teaching materials and shelves for favourite books and toys the child used at play-times.
Materials
A Motivaider®, a pager small enough to fit into a child’s pocket, was used as a tactile
prompt. The device can be programmed to vibrate at different intervals and strength of
Chapter 2
27
vibrations can be adjusted within a range of “1 to 5”. “Rule cards”, that were read with the
children during the training and intervention phases, were created. The rule cards we used
with Alex and Peter (see Appendix 3) contained five questions they could ask of their peers.
For example: “I can get tokens for asking my friends questions. I can say: When is your
birthday? Where do you live? Can I play with you? What’s your favourite TV programme?
Do you have any pets? A buzzer will remind me when to ask a question to a friend.” To help
the children vary their questions, five rule cards with the questions presented in a different
order were used. In accordance with his language skills at the time of the study, a simpler rule
card was used with Reuben who was taught only two initiations: “Hello!” and “Can we
play?”
A token economy reinforcement system was used with all three children who were
already acquainted with its use. Individual token boards contained 10 tokens and were based
on the child’s interests (e.g., tokens had pictures of favourite cartoon characters). We also
used digital timers to measure duration of observations. Data sheets appropriate for event
recording of each dependent measure and for general note-taking, were designed for the
needs of the study.
Dependent measures
Data on two dependent measures were collected: (a) the number of verbal initiations
the target child made towards peers and, (b) the number of verbal responses peers made to the
target child’s initiations.
Verbal initiations were defined as: “audible, appropriate (socially, and in context)
vocal verbalizations, directed towards another person or a group of persons in the absence of
an existing interaction”. An initiation could have the form of a question or a statement, and
did not necessarily need to be a full sentence as long as it could be understood (e.g.
Chapter 2
28
“coming!” or “look!” would be recorded as appropriate). To be characterized as “directed
towards another” the initiation had to be accompanied by some form of non-verbal behaviour
indicating the recipient (e.g., making appropriate eye-contact, or the child’s face being turned
towards the peer while asking a question). Non-appropriate initiations (e.g., utterances out of
context, echolalic phrases) or initiations not directed to another person were not recorded. For
example, when Peter shouted “I am going to crash!” and “I am Scooby!” while riding a bike,
these phrases were not recorded as initiations as they were not directed to anyone in
particular.
Verbal responses were defined as: “vocal verbalizations that are audible, uttered
within 3 seconds of another’s initiation, socially appropriate, and relevant in content to the
initiation”. Responses that were not clearly audible, were inappropriate, had no relevance to
the verbal initiation, or were delayed (longer than 3 seconds after the initiation) were not
recorded.
An event recording system was used for recording both behaviours. Each instance of
target behaviour was recorded as a tally on the data sheet. Additionally, to ensure accurate
data collection (i.e., that an initiation was appropriate), observers took brief notes on the
verbal interactions taking place during the observation period.
Design and Procedure
An ABAB single case design was used and replicated across the three children. Phase
A (baseline) was followed by intervention with implementation of the tactile prompt (phase
B). Then a return to baseline (A) was conducted and finally a second intervention phase (B).
Observations typically lasted for 10 min and were conducted once a day during free-play
activities with peers. A training phase was implemented after the end of the first baseline
period.
Chapter 2
29
Baseline. The child was observed during free-play activities at the intervention setting
(play-yard or indoor play area). Data on the number of verbal initiations the target child made
to his peers and peers’ responses to the target child’s initiations were recorded. No prompts
were given to either the target child or his peers, and when interactions occurred no
systematic reinforcement was provided.
Training phase. To teach the children to respond to the vibrations of the tactile
prompt with social initiations, a systematic teaching procedure similar to the one used by
Taylor and Levin (1998) was designed (Appendix 2). Training sessions were conducted at the
child’s individual teaching area within the autism unit (except for the final 2 stages of the
training procedure). Two training sessions, each lasting approximately 10 min, were
conducted daily by the ABA therapists who normally worked with the child under
supervision of the authors. For each step of the teaching procedure, the child had to achieve a
mastery criterion of five consecutive correct responses before training of the next step began.
It was possible to teach more than one step within a session, depending on individual
progress. Trial-by-trial data were recorded during training. Duration of the training phase was
on average 24 sessions (range 18 - 30).
The token economy reinforcement system was used during the training phase. At the
beginning of the session, the child was informed that he would be earning tokens. Once all
the tokens were collected, he could choose a preferred activity from a list of backup
reinforcers. Reinforcing activities included spending a few minutes of extra play-time in the
school yard, playing a computer game, reading public notices displayed in various parts of
the school, or a trip to the local shops at the end of the day.
The training procedure consisted of eight stages (see Appendix 2). During the first
five, the prompting device was programmed to vibrate at a 30-sec fixed interval (FI).
Chapter 2
30
1. Familiarization with the tactile prompting device. The aim of stage one was to
ensure that the vibration of the pager did not distress or startle the child. Initially, the
Motivaider® was placed on the table and the child was asked to place his hand on top of it,
then it was placed in the child’s pocket with his hand on top of his pocket, and finally it was
in the child’s pocket without the child touching it (i.e., the therapist asked him to place his
hands on the table).
2. Making a verbal initiation when the tactile prompting device was on the table and
the child’s hand on top of it. The aim of stage two was to teach the child to make appropriate
verbal initiations at each vibration of the pager. The therapist told the child they would be
practicing how he could ask questions of his friends and read the rule card with him. Then the
device was placed on the table and every time it vibrated the child was verbally prompted to
ask the therapist one of the questions on the rule card (the therapist said “ask me a question”
while pointing to one of the questions on the rule card). A most-to-least prompting procedure
was followed, so after the child made five correct initiations with the verbal prompt, only the
pointing prompt was used. When this step was mastered, the pointing prompt was faded and
the child was expected to independently ask a question at each vibration. For each correct
response, the therapist provided an appropriate answer to the child’s question and placed a
token on the token board. Correct responses were defined as: “asking a different question on
the rule card on consecutive trials, or a socially appropriate question not included on the rule
card, in a clear voice”. In the case of an incorrect response (e.g., repeating the same question
twice in a row, making a non-appropriate initiation, using unclear speech), the therapist
prompted a correct response. Every five trials, a different rule card was presented to help the
child vary the order of the initiations.
3. Initiations when the device was in the child’s pocket and his hand on top of his
pocket. After reading the rule card with the child, the Motivaider® was placed in the child’s
Chapter 2
31
pocket. At each vibration, the child was expected to make an appropriate verbal initiation to
the therapist. Because of the high levels of prompting used in the previous stage, a least-tomost prompting procedure was used during stage three.
4. Initiations with the device in the child’s pocket and his hands not touching it.
Similar to Stage 3, but this time the child was instructed to place his hands on the table.
5. Initiating while making eye-contact. The aim for this stage was for the child to look
at the person to whom he was initiating.
6. Repeating the question when the other person does not respond. The aim of stage
six was to teach the child to persist when the therapist did not answer his question the first
time. A 45-sec FI was used to allow for time to repeat the question. Reuben did not receive
training on this stage as it was considered to be too advanced for him.
7. Generalization training at the intervention setting. To ensure that all the previously
acquired skills (asking a question when the tactile prompt vibrated with eye-contact,
repeating questions) would be demonstrated outside the training setting, sessions were
conducted at the setting in which the intervention was programmed to take place (playground
or indoor play area). Vibrations of the tactile prompt were programmed at 1-minute intervals.
The child was instructed to play as usually in that setting, and at each vibration of the pager
in his pocket to approach the therapist to ask a question. Correct responses were rewarded
with tokens.
8. Generalizing initiations to a different person, and delayed delivery of
reinforcement. During this final training stage (conducted at the intervention setting similarly
to the previous stage), the child was expected to initiate towards an adult who had not been
Chapter 2
32
involved with the training previously. At the end of the session the therapist “debriefed” the
child and delivered all tokens.
Tactile prompt intervention. The therapist accompanied the child to the intervention
setting (play yard or indoor play area) and together they read the rule card. This reminded the
child that they could be earning tokens for talking to their friends. The child was then asked
to choose for what he would like to exchange his tokens. Next, the prompting device was
placed in the child’s pocket, and programmed to vibrate at 1-minute intervals. For the next 10
minutes, the child played in that setting. The therapist and the person(s) collecting data
observed the child from a distance that would allow them to listen to his verbal interactions
while being as discreet as possible. At the end of the 10-minute period, the therapist
approached the child to debrief him, show him the tokens he had earned, and remove the
tactile prompt. If all ten tokens had been collected, reinforcement was delivered at the end of
the session. In some cases, the child had selected an activity that would take place at a later
point (e.g., a trip to the shops). If not all tokens had been collected during the observation
session, the child was praised for the initiations he had made and was encouraged to try again
to collect all his tokens the next time.
Additional training lasting three sessions at the beginning of the tactile prompt
intervention phase was necessary for Reuben because he would approach an adult (the ABA
therapist who accompanied him in the mainstream setting) and initiate to her when the device
vibrated. Verbal prompts to “talk to a child” were ineffective. Then the therapists were
instructed to ignore Reuben’s initiations to them (avoiding eye-contact as well). If he
persisted initiating to the therapist, she would provide a non-verbal prompt of pointing to one
of the children. This procedure was effective with Reuben, who started initiating towards his
peers.
Chapter 2
33
Fidelity of implementation, and interobserver agreement
Prior to the beginning of the study, a training session with the teaching staff of the
unit was conducted by the authors. The rationale, procedure, and materials of the project were
presented. Role-play with the therapists working in pairs (one playing the role of the child)
was used to help demonstrate the different stages of the training procedure. To ensure
procedural fidelity during the training phase, daily observations of the therapists working
with the children were conducted either by the second (CG) or the fifth author (MS) who
were working as consultant and supervisor in the autism unit respectively.
For interobserver agreement purposes, a second person trained in data collection
observed 24% of baseline and intervention sessions. Inter-observer agreement (IOA) was
calculated by dividing the total number of agreements, by the total number of agreements and
disagreements, multiplied by 100. On average, IOA was 95% (range 80% to 100%). IOA for
individual children was: 93% for Alex (range 80% to 100%), 96% for Peter (range 85% to
100%), and 95% for Reuben (range 90% to 100%).
Results
For all three participants, the number of initiations to peers increased during the tactile
prompt phases (Figure 2.1). During the baseline phases, Alex made on average 0.28 (range 0
to 1) initiations in 10 minutes, whereas when the Motivaider® was in his pocket his
initiations increased to an average of 9.25 (range 7 to 12 during the two intervention phases).
Peter’s initiations during baseline were on average 1.1 (range 0 to 2) and during the tactile
prompt phases he made an average of 6.36 initiations (range 1 to 13) per 10-min session.
Finally, Reuben made no initiations during the baseline phases, whereas during the tactile
prompt phases he made on average 7.87 initiations in 10 minutes (range 5 to 10).
Chapter 2
34
Results relating to peers’ responses to the initiations of the target children show some
variability. Alex received responses to most of his initiations to his mainstream peers.
Sessions 13 and 15 that show a very low number of responses were conducted in a different
play-yard with other children with autism who did not respond to his initiations. For Peter,
many of the sessions were conducted when only children with autism were present in the
play-yard and they usually did not respond to his initiations. Reuben’s peers were younger (3year-old) typically developing children. During the intervention sessions, Reuben would
interrupt his solitary playing at each vibration of the device, approach a peer and saying
“Hello!” He would then go back to the activity in which he had been engaged. Reuben rarely
received a response from the peer, possibly because he did not wait for peers to respond.
15
Baseline
Tactile Prompt
Baseline
Tactile Prompt
13
11
9
Initiations
7
Responses
5
ALEX
3
1
-1
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Chapter 2
35
15
Baseline
Tactile Prompt
Baseline
Tactile Prompt
13
11
NUMBER OF INITIAIONS PER SESSION
9
PETER
7
5
3
Initiations
1
Responses
-1
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21
15
Tactile Prompt
Baseline
Tactile Prompt
13
11
9
7
Initiations
Responses
REUBEN
5
3
1
-1
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17
SESSIONS
Figure 2.1: Initiations to peers and peers’ responses for Alex, Peter and Reuben
Chapter 2
36
Discussion
The results indicate that the use of the tactile prompt combined with prosthetic
reinforcement resulted in all three children increasing their rate of initiations towards peers.
This replicates and extends findings from previous studies. Alex and Reuben made
practically no initiations prior to the intervention. They both initiated at a rate higher than that
expected from typically developing children (one initiation per two minutes, McGrath et al.,
2003) during the tactile prompt phase. Peter had a slightly higher level of initiations during
baseline and his data in the intervention phase show more variability. However, his overall
level of initiations increased considerably during the intervention. Peter sometimes continued
the conversation with the peer after the first initiation. For example during session 8, he had
the following interaction with a typically developing peer:
Peter: “Have you got any pets?” Peer: “Yes, I’ve got a muggy”; Peter: “A muggy? What’s a
muggy?” Peer: “It’s a muggy”; Peter: “But what’s its name?”
Alex often started his initiation with an introductory phrase like: “Excuse me” or “I
have a question for you”. However, he only asked the five questions on the rule card.
Towards the end of the study a peer replied to his initiation with: “You asked me the same
question yesterday.” Given that teaching a larger repertoire of initiations might benefit some
of the children, this was an issue that we targeted in Study 2.
Time restrictions (school closure for the summer vacation) resulted in the termination
of the study at the end of the second intervention phase. We were, therefore, unable to
attempt fading of the prompts (rule card and Motivaider®) and of the prosthetic
reinforcement as was our initial intention. This was a limitation of Study 1 because an
important aim of any behavioural intervention is the removal of artificial stimuli and the
occurrence of the desired behaviour under natural environmental circumstances (Sulzer-
Chapter 2
37
Azaroff & Mayer, 1991). The aims of Study 2 were to replicate the procedures of Study 1
with different participants in a different setting, and to extend the procedure by attempting a
gradual fading of the prompts and reinforcement.
Study 2
Method
Participants, settings and materials
Two children with a diagnosis of autism living in North England, UK, participated in
this study. Both were receiving home-based ABA intervention and were attending school
full-time. Victor was 7 years old and was enrolled in a special needs school. Katie was 9
years old and attended a mainstream school with one-to-one support. Both children were able
to verbally communicate using full sentences and did initiate to adults. Spontaneous
interactions with their peers were limited (e.g., on occasion both Victor and Katie would say
to a peer “play with me!” or “can I play with you?”). IQ and adaptive behaviour measures
were not available for the two participants of this study.
The setting of the intervention for Victor was an Out-of-School club he attended three
afternoons a week with typically developing children. The club had a play area with boxes of
different toys (building blocks, cars, a doll’s house), a role-play area, a kitchen-play area, a
sand play corner, a games console area, and tables for drawing, painting and board games.
The school playground was chosen as the intervention setting for Katie. A box with outdoor
play items such as skipping ropes and balls was available to the children during playtimes.
There were also markings on the ground for playing “What’s the time Mr Wolf?”, hopscotch
and football.
Chapter 2
38
Training sessions for both children were conducted at their homes, during their ABA
sessions with a therapist who normally worked with them. The teaching area consisted of a
table and chairs, bookshelves, a sofa, and a TV set.
Similarly to Study 1, a Motivaider® was used as the tactile prompting device.
Individualized rule cards with questions relevant to each child’s interests and intervention
setting were created. To help the children vary their initiations, a larger number of questions
were included in the rule cards used in Study 2 (Appendix 3). Katie was taught 10 different
questions (e.g., “Do you have a wii?”, “Do you want to have a running race?”, “Do you
want to dance like Britain’s got talent?”), and Victor eight questions (e.g., “What are you
playing?”, “Can I play too?”, “Do you want to play Pirates?”). Token boards containing 10
tokens each, were also used.
Dependent Measures and Design
As in the previous study, the dependent measures were the number of verbal
initiations the target child made to his peers and the peers’ responses to the target child’s
initiations during each 10 min session. A single case ABABCDA design, a variation of a
reversal design, was used. Baseline (phase A) was followed by the implementation of the
tactile prompt intervention (phase B), a return to baseline (A) and a second intervention
period (B). Two fading phases were conducted next; during the first the tactile prompt was
systematically faded (phase C) and then the use of reinforcement was also withdrawn (phase
D). A third baseline phase (A) was implemented after the end of the fading phases. Finally, a
follow-up session was conducted with each participant approximately 6 weeks after the end
of the study.
Chapter 2
39
Procedure
The general procedure was similar to Study 1.
Baseline and tactile prompt phases. These phases were identical to Study 1. Each
child was observed for a 10 min interval during free-play activities with mainstream peers
and data on the target child’s verbal initiations towards peers and peers’ responses to the
target child’s initiations were recorded. Sessions were conducted approximately three times a
week. A variety of preferred items and activities were used as backup reinforcers during the
tactile prompt phase, including access to specific books and magazines, video games, a trip to
the shops, and chocolate.
During the second tactile prompt phase, use of the rule cards was gradually faded.
Because the children were becoming acquainted with their contents, at the beginning of each
session the therapist would give them a choice of whether they wanted to read the card.
During consecutive sessions the children asked for the cards to be read less frequently until
they were not used at all towards the end of this phase.
Training phase. Training was conducted at the end of the first baseline phase and
was identical to the training described in Study 1. Training took place at each participant’s
home, during ABA therapy sessions. Approximately twelve 10-min sessions were conducted
with Katie, and 18 sessions with Victor.
Tactile prompt fading phase. Upon successful second implementation of the tactile
prompt intervention, a procedure of fading the use of the device began. As an initial step, the
interval time between vibrations was increased from a fixed interval (FI) of 1 minute to a FI
of 2 minutes. A second step (implemented during the second session of this phase for Victor,
and the third session for Katie) involved gradually fading the strength of the tactile prompt
Chapter 2
40
vibrations. The Motivaider® vibration strength which had been set at level 3 during
intervention was reduced to level 2, then 1, and then it was placed in the child’s pocket
without being activated. Finally, the device was removed completely. The use of
reinforcement continued as previously during this phase.
Reinforcement fading phase. The aim of this final fading phase was to remove the
use of the token board and the external reinforcement while maintaining a high level of social
initiations. Time constraints (the approaching end of the school year) resulted in this phase
being short. Two sessions were conducted with Victor. Initially, the schedule of
reinforcement was reduced from a continuous one (FR1 ratio – a token for every initiation) to
a variable ratio of 3 (VR3 – a token for approximately 3 initiations). In the next session,
Victor was given a single token at the end of the 10-minute session contingent on his
initiating at the level of a typically developing child (one initiation every two minutes, see
McGrath et al., 2003). A single session was conducted with Katie, and the reinforcement was
reduced from an FR1 ratio to a single token given at the end of the session. Similarly to
Victor, her target was to make approximately one initiation every 2 minutes. The token
economy system was then removed completely and a return to baseline condition followed.
Interobserver Agreement
A second observer, trained in data collection, was present for 25% of observations. The mean
inter-observer agreement across baseline and intervention phases was 97% (range 90 -100%)
for Victor and 99% (range 96-100%) for Katie.
Results
The number of initiations towards peers increased for both children during the tactile
prompt phase (see Figure 2.2). The mean number of initiations during the first and second
Chapter 2
41
baseline phases was 0.22 for Victor (range 0 to 1) and 0.33 for Katie (range 0 to 1) within a
10-minute interval of free play activities. When the tactile prompt was activated, their
average initiations were 10.75 (range 7 to 14) for Victor and 10.4 (range 7 to 17) for Katie
(see Figure 2.2). Improvements were maintained during the phases where fading of the tactile
prompt and reinforcement were carried out. Victor’s data showed a greater variability during
the first fading phase (range 6 to 19 initiations). During the final return to baseline phase,
Victor made an average of 10.3 initiations in 3 sessions and Katie 9 initiations (1 session).
During the follow-up observation conducted six weeks after the last data point, Victor made
15 initiations and Katie 6 within a 10-minute period.
Peers’ responses to the target child’s initiations during the tactile prompt phase
averaged 4.1 (range 1 to 9) for Victor and 5.3 (range 1 to 8) for Katie.
General Discussion
Findings of previous similar studies (Shabani et al., 2002; Taylor & Levin, 1998)
were replicated in both studies. Use of a tactile prompt during free-play activities resulted in
increased frequency of initiations of five children towards their peers. Importantly, the
intervention was conducted in five different settings, which included both indoor and outdoor
free-play areas, equipped in some cases with many and in others with a few play materials. In
addition, training was implemented by different teaching staff and the language skills levels
of the participants varied.
To our knowledge, Study 2 is the first to have achieved a successful removal of the
tactile prompt. In Study 2, when first the pager and then the use of the token board and
reinforcement were systematically faded, both children maintained a high level of initiations
and the gains were still in effect six weeks later. This was an important finding since a
limitation of any prompting method is that when prompts are withdrawn behaviour changes
Chapter 2
21
Baseline
NUMBER OF INITIATIONS PER SESSION
19
Tactile Prompt
Baseline
Tactile Prompt
42
Fading Tactile Prompt
Sr+ Baseline Fol. Up
Fadin
g
17
15
13
11
Initations
9
7
Responses
VICTOR
5
3
1
-1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Chapter 2
43
Sr+ Fading
19
Baseline
Tactile Prompt
Baseline
Tactile Prompt
17
Fading Tactile
Prompt
Baseline
Follow Up
15
13
11
Initiations
9
Responses
KATIE
7
5
3
1
-1
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
SESSIONS
Figure 2.2: Initiations to peers and peers’ responses for Victor and Katie
Chapter 2
44
may not be maintained (Odom et al., 1985). Removal of the tactile prompt has either not been
targeted (Anson et al., 2008; Taylor & Levin, 1998) or has been partially successful (Shabani
et al., 2002) in previous research. Shabani et al. (2002) attempted fading the tactile prompt
with two of their three participants. However, only one child continued to initiate at a
desirable level during the fading phase and initiations of the other child decreased
considerably. Two factors might account for the success of the fading phase in our Study 2.
The first is that reinforcement based on a token system was implemented during the training
phase, and we continued to use it during the intervention period and then throughout the
tactile prompt fading phase. In the Shabani et al. (2002) study, reinforcement was only used
during the training phase. Considering the challenge that social initiations present for
children with autism, it is logical to expect that control of this behaviour may not
automatically be transferred from an external prompt to natural reinforcers such as the
pleasure a typically developing child derives from interactions with other children. Therefore,
it is possible that the use of additional reinforcement played a critical role in the overall
success of the intervention.
The second factor contributing to the success of the fading procedure may have been
the implementation procedure itself during this phase. It is interesting that when the interval
between vibrations was increased from 1 minute to 2, both Victor’s and Katie’s levels of
initiations decreased. When the vibration strength was gradually decreased during the
following sessions, both children had a higher level of initiations. This suggests that fading
the strength rather than the frequency of vibrations might be a more effective way of
removing the tactile prompt while maintaining a high level of initiations. Finally, successful
fading of the tactile prompt and external reinforcement was achieved after an intervention of
a longer duration. The Shabani et al. (2002) study was conducted over 18 to 19 sessions, and
Chapter 2
45
our Study 1 over 15 to 21 sessions. In Study 2, on the other hand, 28 sessions were conducted
with Katie and 35 with Victor (including the follow-up session).
Even with the added time needed for the fading phases, the present research
represents a relatively short and cost-effective intervention. Another advantage of the
intervention is that the procedure can easily be adapted to correspond with individual
children’s needs. For example, the number, length, and content of phrases on the rule cards
can be adjusted and some steps of the training procedure may be omitted if they are too
advanced for the child (as we demonstrated with Reuben’s training and rule card).
Transcripts of individual initiations and responses indicate that quality of interactions
between the target children and their peers differed among participants, although all of them
showed marked improvements compared to baseline. Reuben simply used the initiation
“hello” for the duration of the intervention. However, during the course of the study he
progressed from not having any interactions with peers to confidently walking towards
different children in the play-room and saying “hello” with good eye-contact and a clear
voice. Alex only used the five questions on the rule cards, although he often began his
initiations with a spontaneous introductory phrase like “excuse me” or “I have question for
you”. Peter, Victor and Katie on the other hand, often used their own phrases or adapted the
ones they had been taught. For example, Katie who had been taught the initiation “can I play
too?” asked a peer during session 8 “what else can we play instead of that?” These three
children also sometimes prolonged the interaction by asking more questions on the same
topic.
As reflected in the data on peers’ responses to the target child’s initiations, not all
initiations made by the children with autism were reciprocated by their peers. A partial
explanation is that some of the children’s initiations were statements rather than questions.
Chapter 2
46
For example, in session 16 Victor’s initiations included: “After them Kiam!”, “You’ll go after
him and I’ll go after him!”, “I can’t scare you!” Another consideration is that whereas a
typically developing child makes approximately one initiation every two minutes (McGrath
et al., 2003) the target children initiated at a much higher rate during the intervention. This
might have had a negative impact on the peers’ perception of the child with autism. It is also
possible that in some cases the child with autism made an initiation that interrupted the other
child’s play. An instance during session 8 with Alex illustrates this point. Alex asked a peer
twice “Can I play?” to which the peer responded “Shhh....I am hiding!” Alex’s behaviour
indicates that he had successfully learned to persist when a peer did not respond the first time.
However, he did not perceive that it was inappropriate to initiate to a child who was hiding
during a “hide and seek” game.
Our findings suggest that while the tactile prompt can be effectively used to increase
frequency of initiations other, perhaps more subtle, aspects of social skills also need to be
targeted to ensure that children with autism develop successful social interactions with their
peers. Peer reciprocity is a key element in social relationships (Weiss & Harris, 2001).
Therefore, future research should further investigate this area. It is possible that reinforcing
peers’ responses to the target child’s initiations during the tactile prompt intervention will
result in an increase in responding. An alternative option would be to implement a social
skills training program prior to, or in combination with, the tactile prompt intervention. For
example, Kamps et al. (1992) conducted social skills training within small groups which
included high-functioning children with autism and typically developing peers. They targeted
a variety of social skills such as initiating and maintaining interactions, conversations on
different topics, giving and accepting compliments, helping others and accepting help, and
they found that children with autism and their peers improved their social performance.
Chapter 2
47
A limitation of the present studies is that to listen to the target child’s interactions,
observers had to stand at a relatively close proximity to the child, especially in outdoor
settings. This might have to some degree compromised the non-obtrusive character of the
prompting method. Possibly, attention was drawn to the target child or the spontaneity of
children’s interactions might have been impacted. In future, researchers could consider using
a recording device so that the child’s interactions can be assessed after the end of the
observation period. Audio recording would also allow for a more precise assessment of the
quality of interactions.
In conclusion, the present findings support and extend previous knowledge on the use
of a tactile prompting device to increase the rate of social initiations in children with autism
in free play settings with typically developing peers. Further research is necessary, especially
in the area of improving the quality of interactions between children with autism and their
peers.
Chapter 3
Chapter 3. Teaching Mathematics to Children with Autism: A Systematic Review
48
Chapter 3
49
Abstract
The purpose of this review is to provide a systematic analysis of empirical studies
investigating interventions to teach mathematical skills to students with autism spectrum
disorders (ASD). Sixteen studies were analyzed. Six of these targeted exclusively
mathematical skills and all participants had an ASD diagnosis; the remaining ten studies
included participants without autism and/or targeted non-mathematical skills as well.
Separate analyses of these two categories were conducted. A variety of interventions were
used in the reviewed studies, including different prompting methods, teaching of specific
mathematical skills, and making changes to the environment to facilitate learning. The
majority of studies reported positive results. The methodological strength of the reviewed
studies was evaluated. Implications for practitioners and future researchers are discussed.
Chapter 3
50
Deficits in social and communication development, and the restricted interests of
persons with autism spectrum disorders (ASD), often mean that pupils with ASD have
difficulties functioning in a school classroom (Machalicek et al., 2008). As a consequence,
acquisition of academic skills such as reading, writing and mathematics can be problematic
for these students who might either find the tasks too difficult or lack the motivation to
engage with them (Koegel, Singh, & Koegel, 2010).
Research investigating academic attainment of students with ASD has mostly targeted
literacy skills. Two systematic reviews have explored this area. Chiang and Lin (2007b)
reviewed 11 studies on reading comprehension instruction. A variety of instructional
strategies were used including discrete-trial teaching, incidental teaching, computer-based
video instruction, the use of flash cards, and peer tutoring. The review results indicated that
students with ASD successfully acquired the reading comprehension skills targeted. In a
more recent systematic review on computer-based interventions designed to improve literacy
skills in students with ASD, Sathiyaprakesh et al. (2011) located 12 relevant studies. Literacy
skills targeted included construction of words and sentences, phonological awareness,
reading, and receptive and expressive language. Results however were inconsistent: the
studies using a quantitative analysis produced effect sizes ranging from large to nonsignificant and studies that conducted qualitative analyses reported positive, negative, or
mixed results.
Very little information is available about interventions designed to teach mathematics
to school-aged children with ASD. In a systematic review of school-based interventions for
children with autism, Machalicek et al. (2008) reviewed studies aiming to increase a wide
repertoire of skills, including academics, communication, functional life skills, play, and
social skills. Academic skills were targeted in five studies and in two of these a mathematical
skill was taught. Interventions in the area of academics resulted in positive changes for 78%
Chapter 3
51
of participants. It was not possible to draw any strong conclusions regarding mathematics,
because of the small number of studies that focused on this subject. In their meta-analysis on
teaching mathematical skills to individuals with significant cognitive disabilities, Browder,
Spooner, Ahlgrim-Delzell, Harris and Wakeman (2008) analyzed 68 studies, 12 of which
included participants with an ASD diagnosis. However, no separate analysis of these 12 ASD
studies was conducted.
With the present review, our aim was to address this gap in the literature and to
systematically explore studies that have taught at least one mathematical skill to pre-school or
school-aged students with ASD. Mathematical content includes the following five standards
(areas) according to the Principles and Standards of School Mathematics published by the
National Council of Teachers of Mathematics (NCTM, 2000): (a) The Numbers and
Operations standard involves the abilities of understanding numbers, knowing the meaning of
operations (i.e., addition, subtraction, multiplication, and division), and computing fluently;
(b) Algebra involves understanding patterns and relations among sets of numbers, using
algebraic symbols to represent and analyze mathematical situations, and using representations
such as graphs, tables, and equations to represent quantitative relationships; (c) Geometry
involves understanding the properties of two- and three-dimensional geometric shapes,
describing spatial relationships and solving geometrical problems by applying spatial
reasoning and geometric modelling; (d) Measurement involves understanding the measurable
attributes of objects (i.e., length, volume and weight, time, and money) and being able to
apply appropriate techniques and formulas to determine measurements; and (e) Data Analysis
and Probability refers to the ability to formulate questions and use appropriate methods to
collect and analyze data, and to develop data-based predictions and conclusions.
In addition to mathematical content standards, five process standards refer to ways
mathematical knowledge is built and applied (NCTM, 2000): (a) Problem solving involves
Chapter 3
52
the process of addressing unfamiliar complex situations; (b) Reasoning and proof refers to
processes of analytically investigating mathematical phenomena; (c) Communication refers to
the ability to clearly express and justify mathematical ideas; (d) Connections involve the
ability to synthesize mathematical knowledge from different content areas and everyday life;
and (e) Representations involve the ability to use various ways (e.g., pictures, objects,
symbols, tables) to depict mathematical situations and ideas.
The purpose of the present systematic review was to explore: (a) the mathematical
skills that have been targeted, and the content and/or process standards represented within the
literature with students with ASD; (b) evidence for strategies that have been used for teaching
mathematics to this population; and (c) the methodological quality of research evidence by
using the Scientific Merit Rating Scale developed by the National Autism Center (2009).
Method
Literature search procedure and inclusion criteria
We conducted electronic searches using the ERIC and PsychINFO databases up to
June 2012. Two groups of terms were used: (a) terms for autism including autis*, asperger*,
PDD, pervasive developmental disorder, PDD-NOS, and (b) a list of mathematical terms
(e.g., math*, numer*, number*, count, arithmetic, computation, problem-solving, addition,
subtraction, algebra*, geometr*, measurement, graphing, shape, money, time). Additionally,
we examined the reference list in the Browder et al. (2008) review and conducted manual
searches of studies citing identified articles. Searches yielded over 4000 articles. Titles and
abstracts of these studies were checked by the first author. This initial screening resulted in
the selection of 33 papers that were obtained for a more detailed coding.
Chapter 3
53
We used the following inclusion criteria: (a) Participants had to be pre-school or
school-aged children (3 to 18 years of age); (b) The children had to have a reported diagnosis
of autism/ asperger syndrome/ PDD-NOS (if typically developing children, or children with a
different diagnosis were included, data of children with autism had to be presented
separately); (c) The study had to describe an educational intervention designed to teach one
or more of the mathematical skills defined by the NCTM (2000) standards; (d) One or more
measures of mathematical skills had to be reported as dependent variables; (e) Data
demonstrating changes purportedly due to the intervention had to be available (at a minimum,
a single group pre-test post-test design or an A-B single case design); and (f) The study had
to have been published in a peer-reviewed journal.
Sixteen studies met the criteria for inclusion in the review. The 17 remaining studies
were excluded for the following reasons: (a) Five did not report data focused on children with
an autism diagnosis (Cote et al., 2010; Djuric- Zdravkovic, Japundza-Milisavljevic, &
Dragana, 2011; Everhart, Alber-Morgan, & Park, 2011; Skibo, Mims, & Spooner, 2011;
Vacc & Cannon, 1991); (b) Eight did not involve the implementation of a mathematical
intervention (Allman, Pelphrey, & Meck, 2012; Banda, McAfee, Lee, & Kubina Jr, 2007;
Chiang & Lin, 2007a; Donaldson & Zager, 2010; Gagnon, Mottron, Bherer, & Joanette,
2004; Legge, DeBar, & Alber-Morgan, 2010; Lloyd, Irwin, & Hertzman, 2009; Minshew,
Siegel, Goldstein, & Weldy, 1994). Two additional studies that taught purchasing skills did
not target money computation or value recognition of coins/bills (Gardill & Browder, 1995;
Haring, Breen, Weiner, Kennedy, & Bednersh, 1995); and (c) Two studies did not provide
data on a measure of mathematical skill: Banda and Kubina Jr. (2010) measured the latency
between the time the student was given a non-preferred mathematical task and the time he
started to work on it, and Fienup and Doepke (2008) measured the number of consecutive
fluent responses to known mathematical questions within 3 seconds of the instruction.
Chapter 3
54
Data extraction and coding
Studies that met the inclusion criteria were summarized in terms of the following
features: (a) participant characteristics, (b) setting the intervention was conducted, (c)
research design, (d) NCTM mathematical area(s) targeted, (e) specific mathematical skill
taught, (f) the intervention used, (g) the procedural aspects of treatment fidelity,
generalization and maintenance and (h) the study outcomes (i.e., effectiveness of the
intervention as reported by the authors).
Finally, a more systematic evaluation of the methodological strength of the included
studies was conducted based on the Scientific Merit Rating scale (SMRS) developed by the
National Autism Center (2009). The SMRS is a scoring system designed to evaluate
experimental rigour across five key dimensions: (a) Research design (i.e., the strength of
experimental control); (b) Measurement of the dependent variable (i.e., accuracy and
reliability of data collection); (c) Measurement of the independent variable (i.e., degree of
procedural integrity); (d) Participant ascertainment (i.e., diagnosis provided by independent
evaluators, using established diagnostic instruments); and (e) generalization of treatment
effects (i.e., the degree to which intervention gains were maintained after the end of treatment
and shown to generalize across settings, materials, and persons). Based on the scoring
guidelines of the SMRS each study was given a score between zero and five on each of the
five dimensions, with zero representing a weak and five a strong methodology; then a
composite study score was calculated based on the following weighted formula (National
Autism Center, 2009, pg 23): Research Design (.30) + Dependent Variable (.25) +
Participant Ascertainment (.20) + Procedural Integrity (.15) + Generalization (.10).
Chapter 3
55
Inter-rater reliability
To ensure the fit of the studies against the inclusion/exclusion criteria, an independent
scorer coded the 33 studies that were selected after the initial search, by giving a “yes” or
“no” code for each paper for each of the inclusion criteria. To calculate agreement, the total
number of agreements was divided by the total number of agreements plus disagreements and
multiplied by 100. There was a total agreement between the two scorers (100%).
Additionally, to ensure accurate evaluation of the methodological strength of the
studies included in the present review, a second person trained in the use of the SMRS
independently scored each of the 16 studies. The agreement between the two raters was r =
0.819 calculated by Pearson correlation on the composite score of each study.
Results
Of the 16 studies in the present review, fifteen used a single case experimental design
and one a group design. The studies were published between 1988 and 2011, however the
majority (n = 12) were published between 2008 and 2011. Only six of the 16 studies
described mathematical interventions implemented exclusively with participants with an
ASD diagnosis. The remaining ten studies either included some participants without autism
(typically developing or with a different diagnosis) or targeted skills in other academic areas
as well as one or more mathematical skills. Each of these two categories of studies is reported
separately for ease of reference.
Mathematical Intervention Studies with Children with Autism
Participants and settings
Table 3.1 presents a summary of the six studies; all used a single case design.
Participants were a total of 15 students, 9 male and 6 female. The age range of participants
Chapter 3
56
Table 3.1
Summary of studies aiming to teach mathematics to children with autism
Study
Participants
Setting
Design
NCTM
Mathemati
cal area
Skill targeted
Intervention
Fideli
ty
General
ization/
mainte
nance
Yes/
Yes
Results
SMR
S
score
Akmanoglu &
Batu (2004)
n=3
Chronologic
al Age (CA)
= 6, 12, 17
Special school
Multiple
probe
across
behaviours
Numbers
and
Operations
Pointing to numerals
named by teacher
Simultaneous
prompting
Yes
All participants
acquired skill
3
Ault, Wolery,
Gast, Munson
Doyle &
Elzenstat
(1988)
n=2
CA = 8
Special
education
classroom in
elementary
school
Parallel
treatments
design
Numbers
and
Operations
Answering “What
number?” when
presented with
numeral card
Comparison of
constant time delay
and system of least
prompts procedures
Yes
Yes/
Yes
Both procedures
effective for the 2
participants, a 3rd
participant (no
details known) did
not acquire any
numbers
Touch-points more
effective for all
three participants
3
Cihak &
Foust (2008)
n=3
CA = 7-8
Alternate
treatments
design
Numbers
and
Operations
Solving single-digit
addition problems
Comparison of
number lines and
touch-point
strategies
Yes
Yes¹/
No
Cihak & Grim
(2008)
n=4
CA =15-17
Multiple
probe
across
behaviours
and
settings
Numbers
and
Operations
Independent
purchasing skills:
producing the correct
amount of $ bills by
counting-on
Use of a countingon strategy
Yes
Keintz,
Miguel, Kao
& Finn (2011)
n=2
CA = 6 yrs
Special
education
classroom in
elementary
school
Special
education
classroom in
high school,
school
bookstore,
community
settings
Special
education
preschool
classroom
Yes/
Yes
All three
participants
acquired skill
across settings and
behaviours
4
Pre- posttests
Measurem
ent
Acquisition of
untrained relations
between coins and
their values
Conditional
discrimination
training. Use of
progressive time
delay,
No
NA/
No
One participant
acquired all
untrained relations,
one participant
acquired 4/7
3
4
Chapter 3
Rockwell,
Griffin &
Jones (2011)
n=1
CA = 10
Home
Multiple
probe
across
behaviours
Problem
solving
¹ The generalization procedure did not include fading of the touch point prompts
57
Solving 1-step
addition and
subtraction word
problems
reinforcement
(tokens and praise)
Use of schematic
diagrams
corresponding to
three types of word
problems
untrained relations
Yes
Yes/
Yes
Participant met
criterion for all
three types of
problems
3
Chapter 3
58
was 6 to 17 years. Fourteen of the students had been diagnosed with autism and one with
pervasive developmental disorder.
Five studies were conducted in a special education classroom; in one of these studies
(Cihak & Grim, 2008) which targeted independent purchasing skills, two additional settings
were used: the school bookstore, and a community shop. One study (Rockwell, Griffin, &
Jones, 2011) was conducted at the participant’s home, during the summer vacation.
Research design and measures
A multiple probe design was used in three of the studies, two studies used an
alternating treatments design, and one study used an A-B single case design (Keintz, Miguel,
Kao, & Finn, 2011). The dependent measure used in five studies was the percentage of
correct responses. One study (Rockwell et al., 2011) used a point scoring system with three
points being the maximum score for each problem. Correctly solving of each component of
the problem earned the student a point.
Mathematical areas and skills targeted
The content area of Numbers and Operations was targeted in four studies and the
specific skills taught included identification of numerals (2 studies: Akmanoglou & Batu,
2004; Ault, Wolery, Gast, Munson Doyle, & Eizenstat, 1988), single-digit addition solving (1
study, Cihak & Foust, 2008), and counting-on strategies (1 study, Cihak & Grim, 2008).
Correspondence between coins and their values, from the content area of Measurement was
taught in one study (Keintz et al., 2011). The process area of Problem solving was targeted in
the sixth study by Rockwell et al. (2011) who taught a strategy for solving addition and
subtraction word problems.
Chapter 3
59
Instructional methods and outcomes
In two of the studies, the independent variable was the prompting method(s) used to
teach the specific mathematical skill. Akmanoglou and Batu (2004) used simultaneous
prompting. With this prompting method the teacher consistently provides a prompt together
with the instruction during the training sessions. Thus an erroneous response is prevented.
Acquisition of the skill is assessed during separate sessions (probes) where the task is
presented without the controlling prompt. Findings showed the intervention to be effective
across three students of different ages.
Ault et al. (1988) compared two prompting methods: constant time delay, and a
system of least prompts (also known as least-to-most prompts). During the constant time
delay procedure, the teacher presents the task and waits for a fixed interval (e.g., 3 seconds)
before providing a prompt to the student. With the system of least prompts, initially the
instruction is given without any prompt; if the student does not respond or gives an erroneous
response, the least intrusive prompt is provided. If again the student cannot respond correctly,
the next prompt within the least-to-most prompt hierarchy is provided until the student gives
a correct response. Results indicated that both procedures were equally effective for the two
participants. However, constant time delay resulted in faster acquisition of skills. The
investigators briefly reported that a third participant did not learn any numerals with either
procedure.
In the third study (Cihak & Foust, 2008), the effectiveness of two different teaching
materials to teach single-digit addition were compared. The authors used: (a) a number line, a
ruler-like object containing numerals 0 to 20, and (b) touch-points, numerals with dots on
them (the number of dots correspond, to each numeral, e.g., 1 had one dot, 2 two dots). The
study outcomes showed touch points to be the more effective strategy. The three students
Chapter 3
60
acquired the target skill when this teaching method was used, whereas the number line
strategy was effective but at a slower rate of skill acquisition with one child, partially
effective with the second, and ineffective with the third student.
In the study by Cihak and Grim (2008), students were taught independent purchasing
using the correct amount in US dollar bills. The following skills were trained: (a) choosing
the correct first bill with a value that corresponded to the price of the item (e.g., a $5 bill for
an item priced $9), and (b) counting-on by ones from the value of this bill as they added onedollar bills up to the correct amount they need (e.g., say “5-6-7-8-9” as they count out the
amount of $9). The four students who participated in this study acquired the target skill. A
strength of this study was the fact that the intervention was conducted across three different
settings (i.e., the students’ classroom, the school bookstore, and a community shop).
In the study by Keintz et al. (2011), the researchers trained three relations between
coins and their values (i.e., spoken coin name – printed value, printed value – actual coin,
spoken value – actual coin) and evaluated whether the students would acquire untrained
relations (e.g., spoken coin name – actual coin, actual coin – printed value, spoken value –
printed value). Procedures included a progressive time delay prompting system. For new
tasks initially a prompt was given at the same time as the instruction (i.e., 0 seconds of
delay), then as the student became familiar with the task, the interval between the instruction
and the delivery of the prompt was gradually increased (1 sec., 2 sec., 3 sec., 4 sec., 5 sec.,
etc.). Additionally, two levels of reinforcement were employed: independent correct
responses were reinforced with a token (tokens were later exchanged for a favourite activity),
whereas prompted correct responses were reinforced with. The intervention was effective for
one participant who after being taught on the three first relations acquired all seven untrained
relations. Results of the second participant indicated partial success as he acquired four of the
seven untrained relations.
Chapter 3
61
The sixth study (Rockwell et al., 2011), targeted teaching a student a strategy for
solving different types of word problems which included the following steps: (a) read the
problem, (b) make a diagram corresponding to the problem type, (c) write the number
sentence, and (d) state the answer. The main instructional component was that the student
was taught to create a schematic diagram that helped her identify the correct operation
(addition/subtraction) needed to solve the problem. Data indicated that the intervention was
effective across the three categories of word problems.
Methodological quality
As shown on Table 3.1, out of a maximum score of 5 on the SMRS scale (National
Autism Center, 2009), two studies were given a score of 4 and four studies were given a
score of 3. According to the SMRS guidelines a score of at least 3 points indicates a sufficient
methodological quality that allows for firm conclusions about the effects of the intervention.
Studies Focused on Mixed Participant Groups and/or Mixed Academic Skills
Participants and settings
A summary of the studies that either included participants without autism or taught
non-mathematical as well as mathematical skills is presented in Table 3.2. Ninety three
students in total participated in 9 single case design and one group design studies. Of these,
forty students with ASD received teaching on at least one mathematical skill. Across the
studies, 12 of the ASD participants had a diagnosis of autism, 25 were diagnosed with high
functioning autism, two with asperger syndrome, and one with PDD-NOS. Ages of the ASD
students ranged between preschool (no chronological age specified) and 16 years of age. Six
of the studies were conducted in a special needs classroom and two studies took place in a
regular education classroom. One study was conducted in a separate room off the main
Chapter 3
62
Table 3.2
Summary of studies including participants without autism and/or non-mathematical targets
Study
Participants
Setting
Design
NCTM
Mathematical
area
Skills targeted/
Mathematical skill
taught
Intervention
Fideli
ty
Adcock &
Cuvo (2009)
3 w/ an ASD
(1 w/ autism, 1
w/ Asperger, 1
w/ PDD-NOS)
Chronological
Age (CA) = 7
- 10
Therapy
room in
regular
education
elementary
school
Multiple
probe
across
behaviours
Numbers and
Operations,
Measurement
Preference
assessment, token
economy, most-to
least prompts,
interspersal of
maintenance tasks
among acquisition
tasks
No
Collins, Hager
& Galloway
(2011)
3 w/ moderate
disabilities
(including 1
w/ autism)
CA = 14 yrs
Special
education
resource
room in
middle
school
Multiple
probe
across
behaviours
Numbers and
Operations
Addition of
functional content
(e.g. using
pictures of items
from
advertisements)
Yes
Fletcher,
Boon & Cihak
(2010)
3 w/ moderate
intellectual
disabilities
(including 2
w/ autism)
CA = 13 -14
yrs
2 w/ autism
CA = 9 – 10
yrs
Special
education
classroom
Alternate
treatments
design
Numbers and
Operations
Increasing
performance in
various tasks
(mathematics,
language, following
instructions).
Addition, subtraction,
multiplication, telling
time, value of coins
(child specific tasks)
Increasing
performance in
language, science and
mathematical tasks.
Computing price of
items with tax using a
calculator
Solving single-digit
addition problems
Comparison of
number lines and
touch-point
strategies
Autism
classroom
in
elementary
school
Multiple
probe
across
participant
s
Numbers and
Operations
Increasing attending
to task and academic
accuracy (Solving 1digit multiplication
/subtraction without
regrouping problems)
Self-monitoring
procedure
Holifield,
Goodman,
Hazelkorn &
Heflin (2010)
General
ization/
mainte
nance
No/ No
Results
SMR
S
score
All participants met
criterion across all
different skills
3
Yes/
No
Procedure partially
effective,
ineffective for
mathematical skill
of participant w/
autism
3
Yes
Yes¹/
No
Touch-points more
effective for all
participants
4
No
NA/
No
Attending to task
and accuracy
increased for both
participants
2
Chapter 3
63
Kamps,
Locke,
Delquadri &
Hall (1989)
2 w/ autism
CA = 9, 11 yrs
Special
education
classroom
Multiple
probe
across
behaviours
Measurement,
Numbers and
Operations
Increasing
mathematical,
language and reading
skills. Coin
identification, value
of individual coins
and coin
combinations
Two- choice
discriminating
learning:
discrimination
between 2 sums, e.g.
“touch 1+3”
Solving 1-step
multiplication and
division word
problems
Leaf, Sheldon
& Sherman
(2010)
3 w/ autism
Mathematics:
n=1
CA = 5 yrs
Research
setting
Parallel
treatments
design
Numbers and
Operations
Levingston,
Neef & Cihon
(2009)
1 w/ autism
and 1 typically
developing
CA = 10
Regular
education
classroom
Multiple
probe
across
behaviours
Problem
solving
Polychronis,
McDonnell,
Johnson,
Riesen &
Jameson
(2004)
4 w/
developmental
disabilities,
including 2 w/
autism.
Mathematics:
n=1
CA = 7
Regular
education
classroom
Alternate
treatments
design
Measurement
Academic skills
(mathematics, social
studies). Telling time
at 15 minutes and 30
minutes past the hour
Su, Lai &
Rivera 2010
2 groups
(intervention
and control)
with 34 in
each group
(including 25
w/ highfunctioning
2
preschool
classes for
children
with
autism, 2
integrated
preschool
Control
group prepost- test
Comprehensiv
e mathematic
instruction
Evaluation of the
Project MIND for
children with autism
Typically
developing peers
as tutors
Yes
No/ No
Increase of correct
responding for both
participants
2
Comparison of
simultaneous
prompting and
no-no prompting
procedures
Yes
No/
Yes
No-no prompting a
more effective
procedure for all
participants and
skills
4
Teaching four
pre-requisite skills
(identification of
label, operation,
larger number,
smaller number)
Comparison of
30-minute and
120-minute
distribution trial
schedules of
embedded
instruction using
constant-timedelay and
reinforcement
(praise)
Direct and
embedded
instruction based
on the Project
MIND
Yes
Yes/
No
Performance
increased for both
participants
4
Yes
Yes/
No
Both schedules
were effective
4
No
No/ No
Significant
improvements of
intervention group
at post-test (no
separate data for
children with
autism). Children
w/ autism in
2
Chapter 3
autism)
CA =
preschool age
Waters &
Boon (2011)
64
classes
3 w/ mild
Special
Multiple
Numbers and
Solving 3-digit
intellectual
education
probe
Operations
money subtraction
disabilities
classroom
across
problems with
(including 1
in high
participant
regrouping
w/ autism and
school
s
1 w/ Asperger)
CA = 15 – 16
yrs
¹ The generalization procedure did not include fading of the touch point prompts
Use of touchpoint strategy
Yes
Yes¹/
Yes
intervention group
improved
significantly at
mathematical
reasoning and
problem-solving at
post-test
Intervention
effective for both
participants. A third
participant without
autism did not
maintain his gains
3
Chapter 4
65
regular education classroom (Adcock & Cuvo, 2009) with participants who were fully
integrated in the regular education classroom, and one study was conducted in a research
setting (Leaf, Sheldon, & Sherman, 2010).
Research design and measures
A multiple probe design across participants or behaviours was used in six studies and
an alternating treatments design was used in three studies. A quasi-experimental controlled
design was used in the tenth study (Su, Lai, & Rivera, 2010).
In eight of the 10 studies the dependent measure was the percentage of correct
responses. In another study (Kamps, Locke, Delquadri, & Hall, 1989) a variation of the same
measure was used: instead of a percentage, the number of correct responses (e.g., x correct
responses out of 18 questions asked) was presented. Finally, in the Su et al. (2010) group
design study the mathematical reasoning and problem-solving subtests from the Hawaii Early
Learning Profile (HELP, Parks, 1992) and the Bracken Basic Concept Scale – Revised (1998)
were used.
Mathematical areas and skills targeted
In seven of the 10 studies the following skills from the area of Numbers and
Operations were taught: number identification (Leaf et al., 2010), solving addition problems
(Adcock & Cuvo, 2009; Fletcher, Boon, & Cihak, 2010; Kamps et al., 1989), solving
subtraction problems (Adcock & Cuvo, 2009; Holifield, Goodman, Hazelkorn, & Heflin,
2010; Waters & Boon, 2011), and solving multiplication problems (Adcock & Cuvo, 2009;
Collins, Hager, & Galloway, 2011; Holifield et al., 2010). One study targeted the skills of
coin identification and coin value recognition from the content area of Measurement (Kamps
et al., 1989). Recognising time, another Measurement skill, was targeted in two studies
Chapter 4
66
(Adcock & Cuvo, 2009; Polychronis, McDonnell, Johnson, Riesen, & Jameson, 2004). One
study (Levingston, Neef, & Cihon, 2009) taught solution of multiplication and division word
problems, a skill from the area of Problem solving. Finally, one study targeted comprehensive
instruction with the use of a mathematical curriculum (Su et al., 2010).
Instructional methods and outcomes
Leaf et al. (2010) compared two response prompting methods, simultaneous
prompting and no-no prompting. With simultaneous prompting, a prompt is provided
simultaneously with the instruction to the student (see also previous section on studies
included in Table 4.1). With no-no prompting on the other hand, the teacher initially gives the
student two opportunities to respond independently, then, in the case of two consecutive
erroneous responses, provides a prompt during the third presentation of the task. Findings
indicated that the latter procedure was more effective. The participant acquired all the target
skills taught with no-no prompting and one out of four skills taught with simultaneous
prompting.
Number lines and touch points were two strategies used by Fletcher et al. (2010) to
teach addition tasks, similar to the study by Cihak and Foust (2008) in the previous section of
this review. Results showed touch points to be a more effective strategy than the number line.
The touch point strategy was also used in the Waters & Boon (2011) study to teach
subtraction skills to two students with ASD enrolled in a special education high school class ,
and results were positive.
In the Adcock & Cuvo study (2009), conducted with students enrolled in a regular
education class, the intervention consisted of a package of behavioural procedures which
included: (a) Conducting preference assessments to identify favourite items for each child;
(b) Reinforcing correct responding on acquisition tasks using tokens which were exchanged
Chapter 4
67
for preferred items at the end of the session; (c) Most-to-least prompting procedures:
following an erroneous response, with the next presentation of the task the teacher provided a
full prompt then during consecutive trials less intrusive prompts were used; and (d)
Interspersing easier, previously acquired tasks between acquisition tasks. Implementation of
these procedures resulted in immediate improvements (i.e., the graphs indicated that there
were no overlapping data points between baseline and treatment phases) across students
(n=3) and tasks (addition, subtraction, multiplication, recognising coin values, telling time).
In the study by Polychronis et al. (2004), conducted with a student with autism who
attended a regular education class, embedded instruction was the method used. This is a
procedure that involves distributing instructional trials during other ongoing academic
activities. For example, during a literacy lesson with the whole class, the teacher may conduct
three short individualised teaching sessions with the student with autism. In this study, two
distribution schedules, a 30-minute and a 120-minute schedule, were compared. Instructional
procedures used during both schedules included: (a) a constant time-delay prompting
strategy, and (b) social reinforcement in the form of praise. Results indicated that both
schedules were equally effective. The student acquired both sets of skills, and there was no
difference between the two schedules in the number of sessions needed to reach mastery.
A self-monitoring procedure aiming to increase attending to task and academic
accuracy was the method used by Holifield et al. (2010). The students were taught to record
on a self-monitoring sheet whether or not they were attending to their assigned work when
the teacher gave them a cue to do so. Results indicated that accuracy levels of both students
reached criterion. A weakness of this study was some missing baseline data on one of the two
participants and a very high (Mathematical accuracy = 100%) last baseline data point for the
same student.
Chapter 4
68
Kamps et al. (1989) implemented an intervention involving using typically
developing peers as tutors of the children with autism. Tutors received group and
individualised training, supervision, and feedback from the class teacher. The intervention
resulted in an increase of accurate responding for both participants.
In the Collins et al. (2011) study, intervention consisted of using additional, real-life
stimuli during mathematical instruction. The target skill was calculating the final price of
items by computing and adding tax. To make the task more applied, pictures of items from
advertisements were given to the student as additional stimuli. There was no improvement in
the student’s performance as a result of this addition.
To increase performance in solving word problems that involved multiplication and
division operations, Levingston et al. (2009) taught the student four pre-requisite skills: (a)
labelling the task he had to solve, (b) identifying the operation he needed to perform
(multiplication or division), (c) identifying the largest number of the problem, and (d)
identifying the smallest number. Teaching the first three pre-requisite skills to a mastery level
resulted in acquisition of the fourth skill (identification of the smallest number) and in an
increase of accurate problem solving.
In Su et al. (2010) which was the only study that used a group design, children of the
intervention group received mathematical instruction based on the Project MIND (Maths is
not difficult, Su, 2002). Although the main aim of this study was to evaluate the use of
Project MIND with young children with autism, we were unable to use the between-groups
data in the present review as a number of typically developing children participated in each
group and data of the participants with autism were not analyzed separately. However, the
authors conducted a separate pre- post analysis of the data of participants with ASD in the
intervention group only, which showed a statistically significant improvement on one of the
Chapter 4
69
tests, the Hawaii Early Learning Profile (Parks, 1992). There was no description of the
instruction children in the control group received.
Methodological quality
For the studies in this category, the design field of the quality system was rated on the
basis of the overall study design (i.e., all participants, not just the ones with a diagnosis of
autism, and comparisons across all targeted skills, not just mathematical skills). Out of a
maximum score of 5, four studies were given a rate of 4, four studies were given a rate of 3,
and two studies were given a rate of 2. Scores of 3 or more indicate sufficient methodological
quality and allow for firm conclusions regarding effects of an intervention. A score of 2 on
the other hand, indicates some initial evidence regarding intervention effects but additional
research of a higher methodological quality should be conducted before firm conclusions can
be drawn.
Discussion
A systematic search of the literature yielded 16 studies that focused on teaching
mathematical skills to students with ASD. Not all NCTM mathematical content areas were
represented in the reviewed studies. The area of Numbers and Operations was targeted in the
majority (n=11) of the studies. A few of the studies targeted the basic skill of numeral
identification. However, in most of the reviewed studies (n=8), the more advanced skills of
arithmetic operations were taught (i.e., addition, subtraction, multiplication, and division).
Other skills targeted included time and money skills from the content area of Measurement
(n=4) and solving word problems from the process area of Problem Solving (n=2). We did
not find any studies that taught skills from the content areas of Algebra, Geometry, or Data
Analysis and Probability (NCTM, 2000). Similar findings were reported by Browder et al.
(2008) in their meta-analysis on teaching mathematics to individuals with significant
Chapter 4
70
cognitive disabilities: the majority of research focused on Number and Operations and
Measurement skills.
In seven of the 16 studies the intervention consisted of an Applied Behaviour
Analysis (ABA) strategy (e.g., a prompting strategy) or a “package” of strategies (e.g., a
prompting method and a system of reinforcement). Prompting strategies evaluated included
simultaneous prompting (Akmanoglou & Batu, 2004; Leaf et al., 2010), constant time delay,
system of least prompts (Ault et al., 1988), and no-no prompting (Leaf et al., 2010).
Conflicting results were found by the two studies that evaluated simultaneous prompting to
teach identification of numerals: Akmanoglou and Batu (2004) found the method to be
effective with three participants, whereas Leaf et al. (2010), who compared this method with
no-no prompting, found that the participant acquired only one of the four skills taught with
the simultaneous prompting method. The results of the Leaf et al. (2010) study indicated that
no-no prompting was a more effective method. It is difficult to draw any conclusions on the
most effective prompting method to teach mathematical skills based on the existing evidence.
Generally, the consensus among behaviour analysts with regard to choosing the most
appropriate prompting methodologies is that decisions should be based on students’ learning
profiles and the specific task to be taught (Miltenberger, 2008).
Two studies evaluated a “package” of ABA based procedures in the context of a
regular education classroom. Adcock and Cuvo (2009) implemented a model normally used
in individualized intervention programs with children with ASD consisting of preference
assessments, use of token systems, a most-to-least prompting strategy, and interspersal of
easier, previously acquired tasks among the current targets on which the child was working.
Because a teaching aide supported each child, conducting daily individualized sessions in an
area off the main classroom was a viable option. The number of sessions that participants
Chapter 4
71
needed to acquire a mathematical skill ranged between 6 and 8 and duration of sessions was
20 minutes.
A less intensive model of embedded instruction was used by Polychronis et al. (2004),
also with a student with ASD enrolled in a regular education classroom. With this model the
student remained in the main classroom and during a lesson with the whole class the teacher
conducted an average number of four individualized teaching trials with the child with ASD
and duration of lessons was either 30 or 120 minutes. However, the number of individualized
trials remained the same. Procedures used included a constant time delay prompting strategy
and reinforcement in the form of praise. The student acquired the target skills after four daily
sessions of embedded instruction.
Another study that used a behavioural “package” in the context of a special needs
preschool classroom was the project by Keintz et al. (2011).Preference assessments, token
economies, and a progressive time delay prompting system were the procedures used. Selfmonitoring was another ABA based strategy that was used by Holifield et al. (2010) to
increase attending to task. Academic accuracy in mathematical tasks increased as a result of
the intervention.
The ABA teaching methodologies used in the studies reviewed in the present paper
have been used with children with ASD for decades, and have been shown to be effective in
teaching a variety of academic and non-academic skills. However, the small amount of
research and the variety of methodologies used in the studies included in the present review
allow for only tentative conclusions about mathematics instruction. Reviews of the literature
on teaching mathematics with other populations with disabilities tend to conclude in favour
of ABA strategies. For example, the main conclusion of the Browder et al. (2008) meta-
Chapter 4
72
analysis was the importance of using strategies that included explicit prompt fading
strategies.
In six of the studies, the intervention involved teaching the students with ASD a
specific mathematical strategy or a set of mathematical skills. Skills and strategies evaluated
included: (a) using number lines and touch-points to solve additions and subtractions (Cihak
& Foust, 2008; Fletcher et al., 2010; Waters & Boon, 2011), (b) using a counting-on strategy
(Cihak & Grim, 2008), (c) making a diagram that represented the type of word problem the
student needed to solve (Rockwell et al., 2011), and (d) a set of four prerequisite skills that
helped the student solve word multiplication and division problems (identifying the label of
the problem, the operation they needed to perform, the larger of the two numbers involved,
and the smaller of the two numbers) (Levingston et al., 2009). Positive results were reported
in all studies. However, for most of the interventions it is difficult to draw solid conclusions
as the existing evidence is limited. The only mathematical strategy that was evaluated in three
different studies was the use of touch-points to solve additions and subtractions.
Other interventions implemented included training typically developing peers to tutor
their classmates with ASD (Kamps et al., 1989), and using pictures of items for sale when
teaching tax computation (Collins et al., 2011). The latter intervention did not increase the
student’s accuracy.
A limitation of the present review is that many of the included studies did not
exclusively include students with ASD. There is a possibility that other, similar studies
involving mixed samples might have been published which were not identified by our search
strategy.
According to a classification system developed by the National Autism Center
(National Standards Report, 2009) to help determine the strength of evidence of interventions
Chapter 4
73
implemented with persons with ASD, an intervention can be classified as established,
emerging, unestablished, or ineffective. An established intervention must be supported by: (a)
a minimum of 2 group design or 4 single subject design published studies that include at least
12 participants; (b) the studies should have a score of 3, 4, or 5 on the SMRS; (c) results of all
studies are positive. An emerging intervention should be supported by: (a) a minimum of 1
group design or 2 single subject studies that include at least 6 participants, (b) scores of 2 on
the SMRS, and (c) positive results. Based on these criteria, the only mathematical
intervention included in the present review that exceeds the emerging level of evidence is the
use of the touch-point strategy to solve additions and subtractions. The three studies which
evaluated this intervention included a total of seven students with ASD (Cihak & Foust,
2008; Fletcher et al., 2010; Waters & Boon, 2011). Two of the studies have a score of 4 and
one a score of 3 on the SMRS, and results for all participants were positive. Despite the fact
that further research is necessary before the touch-points strategy can be deemed as an
established intervention, the existing evidence is promising.
In two of the studies the touch-point strategy was compared to that of using a number
line (Cihak & Foust, 2008; Fletcher et al., 2010). Comparisons of the touch-point method to
different strategies should be a focus of future research. From a developmental point of view,
solving an additive task using a number line demands a higher level of mathematical
competence than using touch-points. When working with the number line, the student uses a
counting-on strategy. If he is working to solve the 4 + 3 problem for example, he needs to
find the number 4 on the number line, and then count-on 3 more numbers (i.e., says “4-5-67”). When solving the same task using touch-points, the student starts counting from 1; he
first counts the touch-points of the first numeral (“1-2-3-4”) and he then counts the touchpoints of the second numeral (i.e., says “5-6-7”). Steffe (1992) who conducted extensive
research on early number acquisition, identified certain learning stages in children’s progress:
Chapter 4
74
in the perceptual stage the child needs to see (i.e., perceive) the collection of items he counts;
in the figurative stage he can visualise a collection even if the items are not visible.
According to this model, the touch-point strategy where the child can see, touch, and count
each point one-by-one can be approached by a child whose numeral knowledge is at the
perceptual level. To solve the same task using a number line, however, he needs to be able to
work at the figurative level.
A point that seems to have received limited attention within the existing research is
the development of structured, comprehensive curricula, appropriate for students with ASD.
Possibly one of the reasons that certain mathematical areas identified by the NCTM (2000)
do not seem to be taught to students with ASD (e.g., Geometry and Algebra) is the lack of
corresponding curricula. We only found one study that evaluated a mathematical curriculum
rather than an isolated mathematical skill (project MIND, Su et al., 2010). This curriculum
was implemented with pre-school age children, and there was no information regarding its
suitability for older students with ASD. The availability of curricula that are organized into
progressive levels of mathematical skills would help teachers of students with ASD better
identify the current level of each child’s mathematical abilities and then choose the most
appropriate target skills they need to teach. The combination of comprehensive curriculum
guides with effective teaching methodologies would benefit students with ASD and the
teaching professionals who work with them.
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Chapter 4. An Individualized Curriculum to Teach Numeracy Skills to Children with Autism:
Program Description and Pilot Data2
2
The following persons contributed to the empirical study described in this chapter and will, at times, be
referred to as co-authors: Corinna Grindle, Maria Saville, Richard Hastings, Carl Hughes and Kathleen Huxley
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Abstract
Teaching mathematics to children with autism is an area with limited research evidence. In
this study we developed a teaching manual based on Maths Recovery, a numeracy program
designed for typically developing children. Six children with autism enrolled in an Applied
Behaviour Analysis (ABA) school setting participated in the study and received daily
numeracy teaching over a 20-week period. Our aims were to explore whether Maths
Recovery can be used as a numeracy curriculum for children with autism, evaluate the
progress the children make after a period of intensive teaching, and check for maintenance of
numeracy improvements after the end of the intervention. Using a pre-test post-test design we
found that the adapted Maths Recovery numeracy curriculum was successfully incorporated
within each child’s individualized teaching program, and that all six children improved their
mathematical ability over the course of the intervention. The five month follow up data
showed differences among children, with some of them maintaining their previous gains
while others had a decline. Our data show promising results and support the rationale for
larger evaluation studies.
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Within the research literature on interventions with children with autism, investigating
the best methods of teaching mathematics has received limited attention (Su et al., 2010).
Most existing research has focused on the acquisition of a specific mathematical skill. For
example, receptive identification of numerals was targeted by Akmanoglou and Batu (2004)
who used an errorless teaching method, simultaneous pointing, with three students with
autism aged between 6 and 17. Cihak and Foust (2008) compared two different strategies for
teaching single-digit addition to three elementary school children with autism. The first
involved the use of a number line 1-20; the child found the number representing the first
addend and then moved on for as many numbers as the second addend to find the addition
result. The second strategy employed “touch points”, numerals that have dots on them (one
dot for 1, two for 2, etc). To solve the addition problem the child was instructed to count
aloud the dots of the two addends and then write the last number he/she had said. Touch
points was shown to be a more effective method for all participants. In another recent study, a
10-year-old girl with autism was taught to solve different types of math-word problems
involving addition and subtraction by using schematic diagrams (Rockwell et al., 2011).
Levingston, Neef, and Cihon (2009) explored multiplication and division word problem
solving with two participants one of whom had autism. They found that systematic
instruction on four prerequisite skills (identifying the label of the problem, the operation they
needed to perform, smaller numbers, and larger numbers) resulted in increased correct
problem solving.
One conclusion that can be drawn from this limited literature is that children with
autism can learn isolated mathematics skills. Achieving mathematical competence, however,
involves not just the mastery of a few isolated skills, but a combination of many separate
repertoires. It is important that individual skills be taught systematically as components of a
comprehensive mathematics program (Browder et al., 2008).
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There is a similar paucity of information and research on how to teach mathematics in
curricula described in the autism-focused early intensive behavioural intervention (EIBI)
literature. A number of teaching manuals based on the principles of Applied Behaviour
Analysis (ABA) have been developed to help professionals working with children with
autism systematically teach an array of essential skills (Leaf & McEachin, 1999; Lovaas,
2003; Maurice et al., 1996; Sundberg, 2008). In these guides, considerable emphasis is placed
on aspects of language development, such as understanding receptive instructions, requesting,
using progressively more complex sentences, answering questions, using pronouns, and
prepositions, to name a few. “Learning how to learn” skills (e.g., attending skills, imitation,
compliance with instructions) are also a priority. In the academics area there are generally
more programs targeting reading compared to mathematics (e.g., 6 reading and 2 math targets
in the Advanced Curriculum Guide in Maurice et al., 1996). Program descriptions for listed
targets are brief (e.g., 20 math targets presented within 2 and a half pages in Leaf &
McEachin, 1999). Given the complexity of repertoires required to be competent at
mathematics, a more detailed and systematic teaching tool is needed to help professionals
provide effective mathematics instruction to young children with autism.
One of the key areas in early mathematics is numeracy, or “number and operations”
as identified by the National Council of Teachers of Mathematics (2000). This refers to the
ability to understand and represent numbers, relationships among numbers (place value), and
number operations (addition, subtraction, multiplication, and division). Because numeracy
skills play a significant role in aspects of everyday life such as shopping and managing one’s
finances (Patton, Cronin, Basset, & Koppel, 1997), the question of how best to teach these
skills to children with autism is practically significant.
We concentrated on five criteria in choosing a numeracy curriculum to use and
evaluate, and the Maths Recovery program (Wright, Martland, Stafford, & Stanger, 2006a)
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met all of these criteria. First, the program is designed for young children at the first years of
school, so it is suitable even for a child with no numeracy skills. Second, its development has
been informed by extensive research on how children construct numerical knowledge. Third,
existing data on the program’s use with typically developing children, show it to be effective.
Fourth, it is designed for individualized teaching and therefore adaptable to each child’s
needs. Finally, there are common elements with ABA programs that would facilitate
compatibility with ABA teaching methods so that it could be used in early intervention and
early school-based programs for children with autism. For example teaching strategies like
“micro-adjusting” and “scaffolding” (Wright et al., 2006a , p. 31) are functionally similar to
shaping and prompting/prompt-fading. In addition, most individual teaching activities are
divided into smaller, progressive steps much in the same way as task analysis is used in ABA
programs to break complex skills into teachable units.
Maths Recovery: Description and existing evidence
Maths Recovery was developed in Australia in the 1990s (Wright, Cowper, Stafford,
Stanger, & Stewart, 1994; Wright et al., 2006a), and was intended as a tool for intensive,
individualized numeracy teaching for children in mainstream classrooms who after their first
year in school demonstrated low attainment. The curriculum is divided into five stages with
progressive levels of sophistication: 1. Emergent (the child has few counting skills). 2.
Perceptual (the child can count and do some additive tasks when objects are visible). 3.
Figurative (the child can do additions but, although both quantities are known, the child still
starts counting from one). 4. Counting-on (the child can use counting-on for additive tasks
and counting-back to subtract). 5. Facile (the child can use more advanced strategies rather
than counting-by-ones, such as incrementing and decrementing by tens). Activities for each
stage are grouped into areas called Key topics. For example, the Emergent stage includes the
following Key topics: (a) Number word sequences 1-20, (b) Numerals 1-10, (c) Counting up
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80
to 20 visible items, (d) Spatial patterns (recognising patterns on cards without counting), (e)
Finger patterns (different ways of counting using one’s own fingers) , and (f) Temporal
patterns and temporal sequences (copying and counting patterns of sounds and movements).
Each Key topic includes 3-10 individualized programs. In the Numerals 1-10 Key topic for
example, the child is taught to expressively identify a number on a number card, read number
lines forwards and backwards, place number cards in order, receptively identify numbers
presented in random order, and so on.
The intervention procedure for typically developing children involves the following
steps: 1. A trained teacher conducts an individualised assessment interview with the student
to determine his current numeracy stage. 2. Based on the assessment results, activities from
different Key topics that will help advance the student’s strategies are selected. 3. The
student is taught intensively on an individual basis for 30 minutes a day, 4-5 times a week,
for approximately 12 - 15 weeks. 4. At the end of the intervention period the assessment
interview is repeated. The student then resumes group mathematics instruction with the rest
of his class.
Data from Australian schools (Wright et al., 1994; Wright, 2003), and from other
parts of the world where the program has been implemented, show positive results. In UK
research, 210 low-attaining students received individualised teaching for 20 half-hour
sessions, 3 or 4 times a week (Willey, Holliday, & Martland, 2007). Pre- and post-test data
based on the Maths Recovery assessment tools showed that after intervention 48% of the
participants had gained 2 arithmetic stages, 27% 1 stage, 15% 3 stages, and 6% had remained
at the same stage although they had improved their numeracy skills. A more recent study
conducted in 20 elementary schools in the USA (Smith et al., 2010), was the first Maths
Recovery evaluation study to include a standardised mathematics test in addition to the
program assessment tools. In this project, 343 first-grade students received 30 minutes of
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daily instruction for 4-5 times a week for approximately 11 weeks. A waiting list control
design was used. Significant effects of teaching with Maths Recovery were found, with small
effects (Cohen’s d = .26) on the numeracy subtests of the Woodcock Johnson III (2001) and
large effects (Cohen’s d = .85) on the Maths Recovery assessment test.
In addition to its use as an individualised intervention tool, Maths Recovery has been
used as a model for whole classroom teaching with typical learners. The “Count Me in Too”
numeracy program which has been successfully implemented in hundreds of Australian and
New Zealand primary schools (Bobis et al., 2005) is an adaptation of Maths Recovery, also
developed by Wright (2003). Practitioners in other countries including the USA and the UK
have adopted the model. A strong emphasis is placed on the importance of conducting
continuous assessments of the students’ current level of sophistication to the end that
teaching will be focused “just beyond the cutting-edge” of the children’s knowledge (p.6,
Wright, Martland, & Stafford, 2006b).
The primary aim of the present study was to investigate the feasibility of adapting
Maths Recovery for use with children with autism. We developed a detailed teaching manual
(see Appendix 6) to ensure fidelity of teaching and systematic instructional procedures were
followed with all children. The second aim was to investigate whether intensive
individualized teaching using Maths Recovery would improve the numeracy skills of young
children with autism. A third exploratory aim was to investigate whether any gains the
children made after intervention would be maintained over time.
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Method
Participants
Six boys participated in the study. All had a clinical diagnosis of autism and attended
an autism unit attached to a mainstream school in the UK. This educational provision offered
intensive behavioural intervention based on the principles of ABA (for a description of the
educational model see Grindle et al. 2009; 2012). Their ages at the beginning of the study
ranged between 47 and 81 months (M= 65.67 months, SD= 13.26). Two of the children (Elias
and Liam) were new students in the unit at the time the study began, whereas the rest of the
children had been enrolled for a longer period (e.g., Malcolm and Stuart, a little over 2 years).
To be eligible to participate in the study the children had to be performing below the level
expected for their chronological age in mathematics and to have the following prerequisite
skills: Sitting willingly at a table to engage in learning tasks for short periods of time (up to
15 minutes), following simple one-step instructions (e.g., “clap hands”), matching and sorting
of pictures and number cards, and receptive and expressive labelling of at least 50 objects and
pictures. In addition, so that verbal and motor prompts could be utilized throughout teaching,
the children had to be able to repeat back simple words that they heard (i.e., have an echoic
repertoire) and be able to imitate gross and fine motor movements.
At the start of the study, all six children had some verbal abilities although individual
levels varied and ranged from a using a few single words to talking in full sentences.
Integration in mainstream school was part of the individual program for four of the children
whereas two children did not have integration time at the time of the study; Liam found
transitions to different settings especially difficult and Mike did not have the prerequisite
skills that would have enabled him to benefit from participating in that setting.
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As part of the ongoing annual assessments taking place in the unit (Grindle et al.,
2012), all students were assessed for IQ and Adaptive Behaviour. The tests were conducted
approximately six months prior to the beginning of the study. Five of the children were tested
on the Stanford-Binet Intelligence Scale-Fourth Edition (Thorndike et al., 1986). Mike was
tested on the non-verbal Leiter International Performance Scale-Revised (Leiter-R, Roid &
Miller, 1997) because he did not have the verbal skills to be able to fully understand the
Stanford-Binet. Adaptive behaviours were assessed using the Vineland Adaptive Behaviour
Scales II (Sparrow et al., 2005).
Information on the ages, standardized test scores, and individual characteristics of the
six boys participating in the study is presented in Table 4.1.
Setting
For five of the six students, all teaching sessions were conducted at the child’s
individual work area, typically consisting of a table and two chairs, a variety of teaching
materials, and a collection of favourite toys and books for short breaks between teaching
sessions. For the first 10 weeks of the intervention, Malcolm also received his Maths
Recovery teaching sessions at his individual work area in the autism unit. However, after this
time, he received a combination of one-to-one teaching sessions in the autism unit and group
math teaching using Maths Recovery in the mainstream classroom. Maths Recovery was also
the numeracy curriculum used by teachers in the mainstream school and Malcolm had two
20-minute lessons per week in that setting with his typically developing peers. The setting
was changed for Malcolm because his success at meeting mainstream integration targets
meant that that by the end of the study he was in mainstream school for most of the day.
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Table 4.1
Participant characteristics
Child
IQ score
VABS
Composite
Verbal repertoire
Elias
Age at pretest
(in months)
47
83
68
Aaron
59
61
62
Liam
62
77
57
Stuart
64
89
74
Mike
Malcolm
81
81
51 (Leiter-R)
93
56
79
Sentences ≤ 3
words
Echolalic
words/phrases
Sentences ≤ 3
words
Sentences ≥ 4
words
Single words
Sentences ≥ 4
words
Time in ABA
class
(in months)
2
Mainstream
integration targets
14
20-40
minutes/day
1 hour/week
2
none
14
20-40
minutes/day
none
2-4 hours/day
26
26
Chapter 4
85
Materials
Maths Recovery teaching manual – Autism version. To help promote a systematic
approach to teaching numeracy to children with autism, we developed a teaching manual
based on the book Teaching Number by R. J. Wright et al., (2006a). In keeping with ABA
methodology, for each skill mentioned in the book we:
1. Clearly specified the goals for learning so that they would be observable and measurable.
We also described a mastery criterion as a way of objectively determining whether the goal
had been achieved.
2. Because children with autism do not always easily generalize skills taught, we added a
generalization step to every program to ensure the child could be successful with the task in
different environments, with a variety of materials, or a different teacher.
3. Conducted task analyses on the more complex skills (i.e., we broke down complex skills
into smaller steps for learning).
4. Suggested a systematic approach to instruction by: (a) shortening verbal instructions and
specifying wording for teachers and, (b) including prompting and prompt-fading instructions
for each step of the target skill.
A sample lesson plan is presented in Appendix 6.
Teaching Materials. We used a variety of materials that are part of the Maths
Recovery curriculum, such as counters of different colours, number-lines (1-5, 1-10, 11 – 15,
etc), numeral tracks (number-lines with a small cover for each numeral), number cards for
individual numbers, domino cards with 1-6 dots, and cards with 1-4 dots in irregular patterns.
We created some of these (e.g., numeral tracks, cards with different patterns) based on the
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descriptions provided in the Wright et al. (2006a) book because they have been designed
specifically for Maths Recovery and were not commercially available.
In addition to the teaching materials, token economy systems and a variety of
reinforcing items and/or activities were used for each child. For example, a child would be
working on numeracy tasks for 10 minutes and during this time the therapist would reinforce
appropriate working with placing tokens on his token board. When all the tokens had been
acquired he could choose from a range of preferred activities, which included crafts (e.g.,
painting, collage, making play dough, etc), and favourite toys/games (e.g., Lego™ bricks,
water or sand play, playing in the soft play area, computer games).
Measures
Two main outcome measures were used in the present study.
1. The Test of Early Mathematics Ability 3rd edition (TEMA-3, Ginsburg & Baroody,
2003), is an individually administered standardized test, designed to measure mathematical
ability in children aged between 3 years 0 months and 8 years 11 months. The test includes
both formal and informal tasks, such as verbal counting, counting items, reading and writing
numbers, saying the number that comes after a given number, and story problems involving
additions/subtractions. TEMA-3 yields a raw score representing the number of items the child
answered correctly. The standard score of the test is called the Math Ability Score and is age
referenced with a mean of 100 (SD = 15). A Math Ability Score between 90 and 110 is
described as “average” for a typically developing child. The test also yields an Age
Equivalent Score, or “mathematical age”. For example, a mathematical age of 60 months
indicates that the child performs at the level of a typical 5-year old. The TEMA-3 has two
parallel forms. Form A was used with all participants three times: before intervention, at the
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end of the intervention period, and at follow up five months after post-testing. The test –
retest reliability of Form A is .82 (Ginsburg & Baroody, 2003).
2. The Early Numeracy Curriculum-Based Measurement (EN - CBM, Clarke &
Shinn, 2002; Clarke, Baker, Smolkowski, & Chard, 2008) consists of four subtests, which are
timed and last for one minute each:

Oral Counting (OC): the student counts from one up to as high as he can go in one
minute.

Number Identification (NI): numerals are presented in random order and the student
identifies them.

Quantity Discrimination (QD): the student needs to identify the larger number from a
set of two.

Missing Number (MN): the student is required to identify a missing number from a
sequence of three consecutive numbers.
We made an adaptation to the format of NI, QD, and MN. Typically, the student is
given a page containing boxes with all test items. To avoid the possibility of confusing the
students if too many items were presented simultaneously, every testing item was printed on
a card and was presented to the student separately. This had the added benefit of the numbers
being of a larger font size. We administered the EN-CMB test twice, before the beginning
and at the end of the intervention.
Initial assessment probes. After pre-testing for all children with the standardized
assessments was complete, some more detailed testing on the Maths Recovery skills was
necessary to help determine which skills each child needed to be taught. With intervention
involving typically developing children, an initial assessment interview is conducted.
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Because the level of language used in the interview can be confusing for children with autism
(e.g., asking the child to describe the method he used to solve a task), we substituted it with
probes corresponding to the individual numeracy skills, using simpler, more succinct
instructions. A teacher who knew the child well decided at which developmental Maths
Recovery stage the child would be tested (emergent, perceptual, etc). A therapist was given a
list of the instructions for all the skills in that stage. For each skill two probes were
conducted. If the child answered both correctly, it was assumed that he already had the
particular skill. If he responded incorrectly for both probes, the skill would have to be taught.
In the case of giving one correct and one incorrect response, two more probes were conducted
for the same skill. If any further mistakes were made, the skill would be considered as not
known to the child. Some of the children were tested on more than one stage. During pre-test
trials the child was not given any prompts or corrective feedback. However, to maintain
interest in the task, established reinforcers (e.g., praise, tickles, or short breaks with a
favourite toy) were delivered intermittently between trials.
The assessment probes were intended only as a placement test within the Maths
Recovery program and were not used to assess outcome.
Procedure
Overview of teaching procedure. Teaching based on the Maths Recovery teaching
manual took place daily for approximately 20 weeks. Numeracy targets were incorporated
into the child’s individualized curriculum, and teaching took place in short sessions
throughout the school day. On average, each student received 50-55 minutes of one-to-one
Maths Recovery teaching per week. The therapists who normally worked with the child
carried out sessions. Typically, the child was working on four numeracy tasks from different
key topics at any one point in time.
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The main teaching method employed was Discrete-Trial Teaching (DTT). Using a
one-to-one therapist-child ratio, teaching began with the therapist presenting a cue or
instruction to the child, if necessary prompting a response and finally rewarding correct
responding by providing, for example, praise, the chance to play with a favourite toy, or a
token which could later be exchanged for preferred activities. This single cycle of the
behaviourally-based instruction routine (i.e., antecedent – behaviour - consequence), is
known as a discrete trial. An example of how DTT was used to teach number identification is
as follows: Three number cards were placed on the table in front of the child. Training trials
for each receptive label were initiated by the teacher saying “Touch (number)”. A correct
response was defined as the child giving any selection response (e.g., touching, pointing to,
or picking up number card) within 3 seconds of the start of the trial. All unprompted correct
responses were reinforced immediately. An incorrect response was defined as the child
touching an incorrect number card, doing nothing, touching more than one card, or taking
more than 3 seconds to touch the correct number card. If the child was incorrect, no
reinforcer was delivered and the trial was repeated. This time a prompt would be used, such
as the therapist pointing to the correct number card, positioning the cards in a way that the
correct number card was closer to the child, or physically guiding the child to point to the
correct number. Prompted responses were immediately reinforced with praise. After the child
was successful in solving the task when prompted, the therapist would begin to gradually
remove help (prompt-fading), either by delaying the prompt or by reducing the level of
prompting over consecutive trials until the child provided an independent answer.
Data on each current target was in most cases only recorded once in every teaching
session. The therapist would present the task at the beginning of the session without any
prompts and record whether the answer was correct or incorrect. The mastery criterion for
each skill was three consecutive correct answers across three sessions; a three-day “retention”
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period during which the skill was not taught followed. If the child was still able to correctly
solve the task after the retention period the skill was considered mastered. In some cases,
when a child found a task too difficult, trial-by-trial data were collected at the ABA
consultant’s (CG) recommendation to help keep track of the precise nature of the learning
problem.
Children with autism often do not automatically generalize skills learned at the table
to different teachers, different teaching materials, or different instructions (Ghezzi & Bishop,
2008). Subsequently, we systematically planned for generalization of number skills using
DTT at the table by incorporating a generalization step into every task. For example, if the
child was able to count six counters when sitting at the table, in the generalization step he
would be asked to count six different items (e.g. 6 cars), at a different location (e.g. the play
area), by a different person (e.g. a therapist who did not normally work with him). The skill
was only considered truly mastered when he was able to complete this step without prompts.
Another teaching method employed was frequency building. Thus, as some new
number skills were learnt, time criteria were gradually introduced so that the children had to
answer not only consistently and accurately but also quickly (i.e., fluently, see Binder, 1996).
For example, for the task of expressively identifying numbers, the therapist rotated through a
set of number cards 1 to 10 in random order for 1 minute (all required responses had been
taught previously during DTT). The number of correct responses expected in one minute (i.e.,
“the aim”) was based on the number that a typically developing child of similar age could
achieve. Each child continued frequency building until they met this aim.
Staff Training - Fidelity of implementation
Prior to the beginning of intervention, we conducted two 2-hour training sessions on
Maths Recovery with the therapists from the ABA unit who would be conducting the
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teaching. During this training, the Maths Recovery manual was described completely,
including suggested teaching strategies, directions for data collection, and a list of teaching
materials that would be needed to deliver the program. After this initial training, ongoing
supervision of staff was provided by the second and third author during regular overlap
sessions. During these sessions, therapists were provided with direct feedback regarding their
teaching skills and further advice was given when necessary. This level of training helped to
ensure that the therapists used a consistent approach in their teaching of numeracy skills and
that they had similar expectations as to how each child should respond. In addition, as part of
the regular policy in the ABA unit, fortnightly team meetings were conducted to discuss
individual children’s progress. Any issues around Maths Recovery targets were discussed
alongside the other areas of each child’s program.
To assess treatment fidelity, observations of approximately 5% of teaching sessions
were conducted. Each observation lasted between 3 and 10 minutes and scores on two
domains, treatment fidelity, and data collection fidelity, were recorded. For a treatment
fidelity observation, an observer scored the therapist’s performance on a checklist of
questions regarding the organisation of the session, delivery of instructions, reinforcement
delivery, error correction, and evidence of the child learning during the session. According to
these data, treatment fidelity was on average 87%. For observations on data collection
fidelity, an observer scored whether the child responded correctly to the tasks given to him
and after the end of the session compared these recordings with the data the therapist had
recorded. Data collection fidelity (i.e., observer agreement with the therapist on recorded
data) was on average 93%.
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Results
Pre- and post-intervention and follow-up scores for each child on the TEMA-3 are
presented in Table 4.2. All six children made gains on this test by the end of the Maths
Recovery intervention. The mean Math Ability standard score increased from 66.83 to 78.83
at post-test. Five of the six boys made an improvement of at least eight standard points. One
child (Elias) gained 24 points and reached an age–appropriate level of skill reflected in a
standard score of 100. Age Equivalent scores indicate that prior to intervention, all children
but one (Malcolm) had a math age around three years. After the intervention, they had all
made an improvement ranging between 9 and 15 months. Mean Age Equivalent Scores
improved from 41 months at pre-test to 54.50 months at post-test.
A follow–up test was conducted approximately five months after the end of the
intervention had ceased. With one child, Malcolm, there was a delay of about five additional
months before the follow–up test due to scheduling difficulties. During the period between
the end of intervention and the follow–up test, Elias, Aaron, Liam, and Stuart continued
attending the ABA unit and they received numeracy instruction based on Maths Recovery but
with less intense supervision. Mike and Malcolm had moved to different schools and their
numeracy teaching was based on different curriculum. At the follow–up test, Stuart had
gained another year of math age and eight points on his Math Ability score, Elias and Liam
remained at about the same level, and Aaron and Mike showed a decrease in their scores.
Malcolm kept the gains he had made but, despite showing a slight increase in his raw score
and math age, had a decrease on the Maths Ability score because the rate of improvement
was small compared to the time between the post and follow–up test.
Table 4.3 shows the results of the Early Numeracy Curriculum – Based Measurement
(EN - CBM). Two of the four subtests comprising the EN - CBM subtests were accessed by
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Table 4.2
TEMA-3 test results pre-, post- Maths Recovery intervention, and follow-up
Child
Raw Score
Math Ability Score
Pre-test Post-test Follow up
Age Equivalent (in months)
Pre-test
Post-test
Follow up
Pre-test
Post-test
Follow-up
Elias
1
14
18
76
100
99
<36
51
60
Aaron
0
14
8
63
80
65
<36
51
45
Liam
4
16
17
68
81
77
39
54
57
Stuart
1
10
20
60
68
76
<36
48
60
Mike
1
8
3
<55
56
<55
<36
45
36
Malcolm
25
41
43
79
88
79
63
78
81
Group Mean
5.33
17.17
18.17
66.83
78.83
75.17
41.00
54.50
56.50
SD
9.73
12.04
13.81
9.32
15.34
14.81
10.84
11.91
15.34
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all participants: Oral Counting (OC) and Number Identification (NI). All the children
improved on OC with mean group score per minute increasing from 9.33 at pre-test to 24.67
at post-test. Two children could not count at all at the beginning of the study, and at post-test
the lowest score was 13 per minute. Improvement in NI was more modest (pre-test mean
score 16 per minute, and post-test 27.50). This was an area where the children were relatively
stronger at the beginning of the study. We also found during the intervention period that
reading numerals was the key topic the children mastered most quickly. The fact that children
with autism often possess strong visual skills may account for this. Two children, Elias and
Stuart, were unable to recognize numerals prior to the program implementation. Both showed
significant improvement at post–testing. Aaron and Liam had a small decrease in their NI
performance after intervention, however, they still read about 20 numerals in one minute.
Malcolm was the only child who understood what he was expected to do with the
Quantity Discrimination (QD = the child has to choose the larger number between two) and
Missing Number (MN = the child says the number that is missing from a sequence of three)
subtests. His pre-test scores were 10 per minute (QD) and 8 per minute (MN); at post-test he
scored 15 (QD) and 9 (MN). The remainder of the children were not able to access these tests
at pre-testing and this difficulty persisted at post-testing. There was one exception to this,
Liam, who at post-testing scored 11 per minute on the MN task.
During the course of the study, Malcolm was working on Perceptual stage content and
the rest of the children on the Emergent stage. By the end of the intervention period Elias,
Stuart, Mike, and Liam had mastered all the targets of the “Numerals 1 to 10” key topic, but
were still working on the other areas of the Emergent stage. Therefore, none of the children
gained “arithmetic stages” as conceptualized in Maths Recovery during the intervention
period.
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Table 4.3
EN - CBM test results pre- and post- Maths Recovery intervention
Child
Oral Counting (OC)
Pre-test
Post-test
Elias
0
20
Aaron
7
20
Liam
11
19
Stuart
10
17
Mike
0
13
Malcolm
28
59
9.33
24.67
Mean
10.30
17.02
SD
Note: All values represent number per minute
Number Identification (NI)
Pre-test
Post-test
0
35
25
19
21
20
1
16
15
17
34
58
16
27.50
13.50
16.47
Discussion
In the present study, numeracy teaching based on the adapted Maths Recovery
program was successfully incorporated within the individualized teaching programs of six
children with autism receiving their education in an ABA setting. After receiving systematic
teaching for a period of 20 weeks, all of the children had made gains. Data were also
encouraging in relation to the maintenance of these gains at follow-up. Despite the limitations
of the very small number of participants and the simple pre-test post-test design, we believe
this is the first study to have evaluated a comprehensive numeracy curriculum (i.e., as
opposed to intervention focusing on a specific mathematical skill) with elementary school
students with autism. Our findings therefore have important applied implications.
Probably the most important implication for professionals working with children with
autism is that the Maths Recovery teaching manual was shown to be a tool that can be used to
teach early numeracy to children with different levels of ability. Some of our children had
very little spoken language, or non-existent numeracy skills. However, all of the children
were able to access the curriculum. Another positive aspect was that the structured layout of
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the manual (e.g., complex skills being broken into smaller steps, prompting suggestions being
included in every lesson) and the systematic data collection, made it possible for the teaching
staff both to identify a child’s difficulty with a specific skill and to accommodate for it by
adjusting the teaching procedure. For example, when 12 counters were placed on the table
and Aaron was asked “how many counters?” he would count them by ones (1,2,...12) but was
unable to reply to the next question “good, how many altogether?” A partial phonemic
prompt (e.g., the therapist saying “tw....” immediately after asking the question) was
introduced; then over the next trials the task was presented the therapist would aim for an
independent answer. In another program when the child and the teacher take turns saying one
number each (e.g., teacher: “1”, child: “2”, teacher: “3”), the visual prompt of a ball being
passed back and forth between the two was used to help Aaron know whose turn it was to say
the next number. For Liam, who would often make errors when sequencing number cards,
initially the therapist would place the first number card (e.g., 1 for numbers 1-5) and Liam
would continue with the rest of the cards. After he was successful with the task with this
prompt, the therapist would start withholding this help so he could solve the task
independently. With another child who found this task (sequencing number cards) more
challenging a backward chaining procedure could have been used instead. The initial step
would involve the therapist ordering the first 3 number cards (1-3) and then the child
completing the sequence with numbers 4 and 5; as a next step two number cards would be
ordered by the therapist and the last three by the child, and so on, until the child was able to
sequence all five number cards by himself.
Regarding the children’s numeracy progress following the intervention, the results
suggest that effects were positive. Improvements on the TEMA-3, which assesses a variety
of skills, give a more general picture of a child’s numeracy level, as indicated by the Maths
Ability and Age Equivalent (mathematical age) scores. At the beginning of the study, five of
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the six children demonstrated very low numeracy skills, and four of them performed below
the level of a 3-year old child. They were, for example, unable to complete simple tasks such
as counting 3 cats in a picture or 5 digits on one hand. Following intervention, all of the
children except Mike had a mathematical age of more than four years and were able, amongst
other skills, to count about 20 items one-by-one, recognize patterns such as four dots in a dice
configuration without counting, and show the required number of digits.
The EN-CBM subtests offer a glimpse into the children’s performance on a few
specific skills. All six children showed improvements in their counting skills (OC, minimum
score 13) and were able to recognize written numbers (NI, lowest score 16 numbers per
minute) after being taught with Maths Recovery. There were almost no changes on their
ability to identify the larger of two numbers (QD) and the missing number from a sequence of
three consecutive numbers (MN). According to Clarke et al. (2008) these two subtests (QD
and MN) require more complex strategies than OC and NI. It is possible that, in spite of their
progress, the children did not reach the arithmetic level required for these tasks, a hypothesis
that is supported by the math age scores on the TEMA-3. At the end of intervention the
mathematical age of the five children who did not access the QD and MN subtests was
between 3 years 9 months and 4 years 6 months. The EN-CBM tasks are intended for
kindergarten age children (ages 5 to 6 years). Malcolm, the only child who could access both
QD and MN, had a higher mathematical age of 5 years 3 months (pre-test) and 6 years 6
months (post-test). Another consideration with QD and MN is that these skills had not been
specifically targeted during intervention. Although the children had worked on similar skills,
for example, putting number cards in order, this knowledge was not generalized to the new
tasks (e.g., missing number) with the exception of Liam.
Individual gains on outcome measures showed variability (e.g., Math Ability gains
range between 1 and 24 points), suggesting a different pace of learning among participants.
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The youngest of the children (Elias, 4 years old) made the greatest improvement: his Math
Ability score increased by 24 points, and he reached age appropriate levels as indicated by
both the Math Ability (100) and the Age Equivalent (chronological age = 4 years, 7 months,
maths age = 4 years, 3 months) scores at post-testing. Improvements of the other five children
were considerable although less dramatic. Even when the gains were small, however, it is
encouraging that the child made some progress in an academic area which many typically
developing children find difficult. Mike, one of the older children in the group (6 years, 9
months) increased his Math Ability score by just one point. However, as indicated by his Age
Equivalent scores, prior to intervention his numeracy skills were lower than those of a 3-yearold child, so it is noteworthy that six months of teaching using this approach helped him gain
at least 9 months in mathematical age—an improvement that would be considered positive
for a child without learning difficulties. Additionally, according to anecdotal reports from his
mother, Mike was generalizing his newly acquired numeracy skills and using them at home
by singing counting songs, counting pictures of items, and recognising numbers in books;
these were things he had not been doing prior to the study.
In contrast with findings from previous research conducted with typically developing
children (Bobis et al., 2005; Willey et al., 2007) our participants did not gain any Maths
Recovery arithmetic stages. Although the very small number of participants makes it
difficult to draw any solid conclusions on why this maybe the case, the fact that children with
autism often have additional learning difficulties might account for a slower pace of learning
compared to typically developing children. There was also an important difference between
our study and the other projects evaluating Maths Recovery. We used the program as the sole
numeracy curriculum for the six children, some of whom had never before been exposed to
any mathematics teaching. In the projects with typically developing children, the intervention
is being offered to children who have already have had some group teaching in the
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mainstream classroom. Consequently, previously acquired numeracy knowledge levels
differed between our children and the participants in other Maths Recovery evaluation
studies.
The final aim of the project was to assess whether the children would maintain the
post-intervention gains after the end of the project. The follow-up test, conducted 5 months
after the end of the study (10 months later for Malcolm) showed that three out of the four
children who continued to be taught with Maths Recovery but under less strict supervision,
continued to make gains and their Maths Ability standard scores were stable (Elias and Liam)
or had increased (Stuart). The fourth child (Aaron) had a decline in his skills and was often
non-responsive during the follow-up test. Of the two children who moved to a different
school environment after the end of the Maths Recovery project, and were therefore being
taught with different mathematics curricula, Malcolm had kept all the gains he had made at
post-testing and had made some further progress. For example, he was able to solve addition
(6+3, 4+4) and subtraction (2-1, 8-4) tasks by counting-on and counting-back, which he had
not been able to complete at post-testing. Mike, on the other hand, had lost many of his
acquired skills and his score decreased to nearly as low as his pre-intervention level. It is
possible that these numeracy skills had not continued to be targeted in the new school
environment and, as a result, had not been maintained. This finding supports a practice
implication that educators working with children with autism revisit mastered targets from
time to time and ensure their maintenance.
Further research is needed to extend our pilot findings by examining the effectiveness
of the program over a longer period of time, with larger samples of participants, and
including a control group in the study design. Another consideration would be to explore the
use of the curriculum with different populations (e.g., children with intellectual disabilities).
Finally, it would be interesting to assess whether the curriculum could be used in standard
Chapter 4
special educational settings that are not ABA-specific and may not have the kind of staff
student ratios or the expertise in behavioural methodologies (e.g., prompting and promptfading) common in these settings.
100
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101
Chapter 5. An Individualized Numeracy Curriculum for Children with Intellectual
Disabilities: A single blind pilot randomized controlled trial3
3
The following persons contributed to the empirical study presented in this chapter and will referred to as coauthors: Richard Hastings, Corinna Grindle, Carl Hughes and Zoë Hoare
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Abstract
Research investigating structured, comprehensive numeracy curricula that can be used with
children with Intellectual Disabilities (ID) is limited. We evaluated an adaptation of the
Maths Recovery program. Twenty four elementary school children with severe ID or autism
were randomly allocated into the intervention and control groups with twelve children in each
group. For 12 weeks, children in the intervention group received individualized numeracy
teaching based on the adapted Maths Recovery curriculum, whereas children in the control
group received “mathematics as usual” teaching. Pre- and post- intervention tests on
standardized numeracy measures were conducted. Results indicated that the Maths Recovery
group made significant improvements at post-intervention in comparison to the control group.
A follow-up test showed that gains were maintained seven months after the end of the
intervention. Implications for practice are discussed.
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One of the main mathematical domains defined by the US National Council of
Teachers of Mathematics (NCTM, 2000) is numeracy (or numbers and operations).
Numeracy involves being able to understand and represent numbers, relationships among
numbers (e.g., place value), and number operations (addition, subtraction, multiplication, &
division). Mathematics is a curriculum area that many students with intellectual disabilities
(ID) find difficult, and they often do not acquire even the basic numeracy skills during their
school years (Buttler et al., 2001). These deficits impact vital areas of everyday life such as
being able to use money or understand quantities. Therefore, limitations in numeracy may
affect a person’s quality of life into adulthood (Ayres, Lowrey, Douglas, & Sievers, 2011;
Patton et al., 1997; Rivera, 1997).
Although attention given to numeracy instruction within the field of educational
research for students with special educational needs has been increasing in recent years
(Gersten et al., 2009), most of the published studies have focused on children who have mild
disabilities or are “at risk” of later disabilities (Gersten et al., 2009; Kroesbergen & Van Luit,
2003; Miller, Buttler, & Lee, 1998). In a systematic review, Buttler, Miller, Lee, and Pierce
(2001) located 16 studies on mathematics interventions for students with mild to moderate ID
spanning a 10-year period (1989-1998). Buttler et al. concluded that explicit instruction,
frequent feedback and repeated opportunities for practice were successful methodologies with
this group of children. Another finding of the review was that the majority of studies targeted
the relatively more advanced mathematical skills of computation (number operations) and
problem-solving, thus moving on from the tradition of teaching mostly basic skills (e.g.,
number recognition, counting) to this population.
Focusing on mathematical interventions for students with significant cognitive
disabilities, Browder et al. (2008) reviewed 68 studies published between 1975 and 2005.
Participants had diagnoses of moderate/profound/severe ID or autism. Of these, 54 involved
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single subject designs and 14 used a group design. Just over a half (54%) of the included
studies targeted numeracy skills (e.g., counting, matching numbers, calculations). Browder et
al. (2008) found only 17 studies that focused exclusively on participants with severe or
profound ID; 6 of these focused on teaching numeracy skills: counting (2 studies), matching
numbers (2 studies), and number operations (2 studies). The overall conclusion of Browder
et al.’s review was that systematic instruction, including clearly defined teaching goals,
prompting and prompt-fading strategies, was the general procedure associated with the best
outcomes.
Despite a body of literature and helpful reviews, the information presently available to
practitioners working with students with ID is limited in a number of areas. For example,
most studies have focused on teaching a specific skill such as counting items or matching
numerals. Information is scarce in terms of structured and comprehensive curricula
appropriate for this population that would help practitioners teach all numeracy domains.
There is some research on the use of the TOUCHMATH program (Bullock & Walentas,
1989), a commercially available program that employs numerals with the equivalent number
of dots on each numeral (i.e., one dot on 1, two dots on 2 etc.) to teach number operations
(addition, subtraction, multiplication, and division). Using this program, students touch each
dot as they count forwards or backwards. The existing evaluation studies on TOUCHMATH
for children with ID have focused on teaching addition and subtraction skills to students with
mild or moderate ID. Scott (1993) used the program to teach addition and subtraction to two
elementary-aged children with mild ID. More recently, the program was used to help three
high school students with mild ID learn to solve 3-digit subtraction problems involving
money (Waters & Boon, 2011). In another project, Fletcher, Boon, and Cihak (2010) used
TOUCHMATH to successfully teach addition to three middle school students with moderate
ID. Fletcher et al. demonstrated that the TOUCHMATH program was more effective than an
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alternative strategy, that of using a number line. We could find no existing research on the
effectiveness of the program across a wider range of numeracy skills.
In the research literature on teaching mathematics skills to children with ID, there are
few high quality group design studies (i.e., randomized experimental designs including a
comparison or control group). Another methodological weakness is the limited use of
standardized measures - most researchers have used measures corresponding to the specific
skill targeted in the intervention. For example, only two of the 14 group studies included in
the Browder et al. (2008) systematic review used standardized measures.
In our previous research on numeracy interventions with children with autism, we
found a similar shortage of structured, comprehensive curriculum guides that can be used by
practitioners to systematically and effectively teach these children. We adapted an existing
numeracy curriculum, the Maths Recovery program (see Chapter 3 of the present thesis).
Maths Recovery is a curriculum that has been originally designed for typically developing
children who were performing poorly in mathematics (Wright et al., 2006b) and has been
successfully implemented in several countries (Smith et al., 2010; Willey et al., 2007; Wright,
2003). The program covers numeracy skills ranging from very early (e.g., counting 1-20,
recognizing numerals 1-10, being able to count up to 20 items, counting using fingers) to
advanced (e.g., counting by 10s and 100s to 1000, addition/subtraction of two-digit numbers,
word problems involving multiplication/division). We used Maths Recovery to conduct a
preliminary evaluation study with six children with autism who were enrolled in an Applied
Behaviour Analysis (ABA) autism setting. Comparisons of pre- and post-intervention scores
using standardized numeracy measures showed that, after 20 weeks of intensive one-to-one
instruction, all six children had improved their numeracy skills and had made gains of
between 9 and 15 months of mathematical age.
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The purpose of the present study was to extend our previous research by using Maths
Recovery with children with severe ID who do not have autism. We also adopted a strong
experimental design and a larger number of participants than our initial autism research. We
employed a waiting list control group design and compared the progress of a group of
children who were taught individually with Maths Recovery to that of a similar group of
children who received “mathematics as usual” teaching within the school setting. We
conducted the present study in a special needs school, where the ratio of staff to children was
much lower than the one-to-one typical for ABA settings and where there was limited
awareness of ABA teaching methodologies. Our aims for this study were, therefore: (1) To
determine whether children with severe ID who were taught individually with the Maths
Recovery program, would make better numeracy progress than a similar group of children
who received instruction with the mathematics curriculum used by the school, and (2) To
explore whether any numeracy improvements for the intervention group would be maintained
over time.
Method
Participants and setting
Twenty four elementary school children participated in the study. Twelve received
one-to-one numeracy teaching with the Maths Recovery model and 12 continued with
“mathematics as usual” instruction within their classrooms. All were attending a special
needs school in North Wales which serves students with severe intellectual disabilities. The
children had been identified by their class teachers as requiring support with mathematics.
Nineteen had a diagnosis of severe ID and five were diagnosed with an Autism Spectrum
Disorder (ASD). Eleven of the twenty four children had an additional medical condition. All
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had some verbal capabilities ranging from using single words to being able to talk in full
sentences. Descriptive information about the two groups of children is provided in Table 5.1.
Table 5.1
Participant Characteristics
MR group
Control group
Variable
(n=12)
(n=12)
Male
7
9
Female
5
3
Range
75-132
69-134
Mean
100.25
100.00
SD
18.93
20.42
Severe ID
9
10
Autism
3
2
ADHD
1
-
Epilepsy
-
1
ADHD & Epilepsy
-
1
Microcephaly
1
-
Fragile X syndrome
-
1
Down syndrome
-
1
Rubinstein-Taybi syndrome
1
-
Chromosome 6 deletion
-
1
Spina Bifida & Hydrocephalus
1
-
Cerebral Palsy
1
1
Gender
Age in months
Main Diagnosis
Additional Diagnoses/ Medical
conditions
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Interventions
The Maths Recovery Model
The Maths Recovery early numeracy curriculum is based on an instructional
framework (Wright et al., 2006a; 2006b) consisting of five progressive stages of
sophistication:
1. Emergent Stage: the child has few counting skills. Instructional targets include facility with
number word sequences up to 20, numerals 1 to 10, counting collections of visible items,
spatial patterns up to 6 (e.g., recognizing dice-like configurations without counting the dots
one-by-one) and finger patterns (counting using one’s fingers).
2. Perceptual Stage: the child can count and solve some additive tasks when items are visible.
Targets for this stage include number word sequences to 30, numerals up to 20, doing
additive tasks involving screened collections of items, more advanced spatial and finger
pattern activities and some basic multiplication and division tasks using items.
3. Figurative Stage: when solving additive tasks the child counts from one. Target skills
include word sequences and numerals to 100, counting-on and counting-back to solve
additive and subtractive tasks and facility with partitions of 5 and 10.
4. Counting-on and Counting-back Stage: the child can solve additive task by counting-on
and subtractive tasks by counting-back. Target skills to further his numeracy abilities include
number word sequences by 2s, 3s, 4s, 5s and10s in the range 1-100, numerals up to 1000,
incrementing and decrementing by 10s and 1s, adding to and subtracting from decade
numbers, multiplication and division tasks.
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5. Facile Stage: the child can count by 2s, 3s, 5s and 10s. Skills targeted include number word
sequences by 10s and 100s off the decade, two-digit additions and subtractions and advanced
multiplication and division tasks.
Activities within each stage are grouped into Key Topics (numeracy areas). For
example, the Emergent stage includes the following Key topics: (a) Number word sequences
1-20, (b) Numerals 1-10, (c) Counting up to 20 visible items, (d) Spatial patterns (recognising
patterns on cards without counting), (e) Finger patterns (different ways of counting using
one’s own fingers), and (f) Temporal patterns and temporal sequences (copying and counting
patterns of sounds and movements).
To make the Maths Recovery curriculum more easily accessible by children with
developmental disabilities we developed a teaching manual (described in more detail in
Chapter 3 of the present thesis; see also Appendix 6) containing all the activities described in
the Wright et al. “Teaching Number” (2006a) book. The following modifications were made
to each target skill:

The learning goal was clearly specified. To help practitioners determine when this
goal was achieved, a mastery criterion was also described.

An additional generalization step was added to every task to ensure the child could be
successful with the task with a variety of materials, in multiple environments and with
a different teacher. This addition was especially important for children with autism
who often need help with generalizing acquired skills.

Some complex skills were broken into smaller steps to facilitate teaching and
learning.
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
110
We developed a more systematic approach to instruction by: (a) shortening verbal
instructions and specifying phrases for teachers to use, and (b) including prompting
and prompt-fading instructions for each step of the target skill.
A further modification to the procedure followed by Wright et al. (2006a; 2006b)
involved the assessment of the child’s level of numeracy skills prior to the intervention. With
typically developing children, an assessment interview would normally be conducted during
which the teacher would often ask the child to describe his strategies for solving a task. We
conducted a probing session instead, presenting instructions to the children in a simpler and
more succinct language. The child was asked 2-3 questions corresponding to each skill listed
in the manual. If he/she answered correctly the skill was considered known to the child,
otherwise it had to be taught. The purpose of this probing session was to help us determine
which Maths Recovery skills we would teach each child and this procedure was not part of
the study outcome measurement. All probing sessions with the children in the intervention
group were conducted by the first author. No feedback was given to the child during these
sessions (i.e., regarding correct or incorrect responding); we did however reinforce him/her
for attending and working nicely with praise and short breaks with a favourite activity.
Based on each child’s performance on the Maths Recovery probes, numeracy lessons
from different areas of the Maths Recovery manual were chosen. For example, a child’s
targets could include: (a) Counting from 1 to 10, (b) Reading a number-line 1 to 5 forwards
and backwards, (c) Count 3 to 5 fingers sequentially without looking at his fingers, and (d)
Counting collections consisting of 6 to 8 items. For most of the children, targets from the
Emergent stage similar to the ones just mentioned were chosen. A small number of children
who had more advanced numeracy skills were able to access the Perceptual or the Figurative
stage and were working on tasks such as counting forwards up to 100, counting backwards 30
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to 1, adding the items of two collections when one collection was screened, or ordering
number cards in the range 30 to 100.
For the 12 weeks of intervention, the children in the Maths Recovery group received
one-to-one numeracy teaching following the manual. The intervention was delivered either
by a teaching assistant who worked in the child’s classroom or by the first author who is a
qualified teacher and offered to undertake some of the teaching in classes that had many
children participating in the study. Teaching took place in different quiet areas within the
school. In most cases, a small room off the main classroom was used. For a few children, a
quiet area within the classroom was used instead.
We used a Discrete-Trial Teaching (DTT) procedure. Each discrete trial comprised
three components: the teacher’s instruction to the child, the child’s response (which could be
prompted by the teacher if necessary), and finally the teacher rewarded correct responding by
providing a high five, praise, a short interval of playing with a toy, or a token which could
later be exchanged for a favourite activity. When the child was unable to complete the task,
the instructor would present the same task in the next trial with a prompt, thus partially
helping the child to respond. Once the child was able to respond correctly when the prompt
was provided, the instructor would attempt the removal of the prompt (prompt-fading) during
following presentations. Prompting and prompt-fading directions for each skill were included
in the manual (Appendix 6). In some cases, when a child had persisting difficulties with a
task additional prompting suggestions were discussed by the intervention team. As DTT
allows for a fast pace of teaching, the child had many opportunities to work on each of their
four numeracy targets throughout the session. The instructors varied the order in which the
tasks were presented. In addition, as the children progressed in their learning targets,
questions on previously mastered skills were intermittently asked to ensure retention of those
skills and to vary the level of difficulty of the tasks within the session.
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Data on each of the child’s targets were recorded once in every session. The instructor
presented the task to the child without prompting and a correct or incorrect response was
recorded on the data sheet for the skill. The mastery criterion for each skill (or sub-step of a
skill) was three correct answers across three consecutive sessions.
Table 5.2
Number of session and total instructional time for children of the intervention group
Cases
Sessions
Total duration (min)
Child 1
13
210
Child 2
13
265
Child 3
14
225
Child 4
15
305
Child 5
19
350
Child 6
21
255
Child 7
22
420
Child 8
22
425
Child 9
24
390
Child 10
31
590
Child 11
33
620
Our initial intent was for every child to have 4-5 intervention sessions per week.
However, this did not prove to be possible in practice. Intensity of intervention was,
therefore, variable. Some of the children had as few as 13 individualized sessions in total
whereas others had over 30 teaching sessions during the course of the study. Sessions
typically lasted between 15 and 20 minutes. Thus, total instructional time for the children in
the Maths Recovery group ranged from 3 hours 30 minutes to 10 hours 20 minutes. Detailed
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information on the number of sessions and total instructional time each child received is
presented in Table 5.2.
Training the school staff to implement the Maths Recovery intervention involved a
number of steps. Initially, two 2-hour training sessions on the program were conducted by the
first author with the teaching assistants who would be delivering the intervention. The
teaching manual, materials and teaching procedures were discussed during these initial
sessions. As a second step, after pre-testing with the standardized measures and the Maths
Recovery placement probing were complete, one or two teaching sessions were conducted
with each of the intervention group children and the teaching assistant who would be working
with the child. During these individualized training sessions, the first author modelled
teaching each the child’s targets and the teaching assistant had the opportunity to practice
teaching and discuss any questions about the procedure. Once the teaching assistant felt
confident about delivering the intervention, he/she took over the child’s teaching. Throughout
the course of the study, formal and informal meetings between the teaching assistants and the
first author were conducted to discuss issues concerning individual children’s progress.
Each teaching assistant worked with one or two children. For two of the classes, the
first author taught some of the children. The same person throughout the study taught the
same child.
Mathematics as usual teaching
Children in the control group had four to five 1-hour sessions of mathematics teaching
per week as a part of the typical mathematics instruction in the school. At least two of these
sessions covered numeracy targets. Typically, each session started with whole-class activities
which included oral counting, identifying numerals, counting groups of items, or copying
patterns of sounds. The children were then divided into small groups where they engaged in a
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variety of numeracy activities (e.g., sorting numerals, matching numerals to quantities).
During the remaining weekly sessions, the children received instruction on other
mathematical components such as measurement and geometry.
Materials
We used a range of teaching materials that correspond to the various Maths Recovery
skills. For example, materials for teaching Key Topic 2 (numerals) included number cards for
individual numbers, number lines (1-5, 1-10, 11 – 15, etc), numeral tracks (number lines with
a small cover for each numeral), and the 100-square (a 10 x 10 square containing numbers 1 –
100). Collections of items such as counters and laminated pictures of items such as cars,
dolls, and insects were used for the skills of Key Topic 3 (counting visible items). Domino
cards with 1-6 dots and cards with 1-4 dots in irregular patterns were used with other
resources for Key topic 4 (spatial patterns).
In keeping with ABA teaching methodology, a variety of items and activities were
used as reinforcers for each child based on his/her preferences. Insert and jigsaw puzzles,
story books, bubbles, small toy cars, animals, building blocks, colouring pencils and drawing
books were some of the items that we used. With some of the children, a token board system
was also utilized. Tokens were placed on the board contingent on appropriate working. When
all the tokens had been acquired, the child could choose one of the reinforcement
items/activities and engage with it for a few minutes. A 20-minute teaching session could
include three 5-minute intervals of work on the child’s numeracy targets with two minutes of
play at the end of each interval. A few of the older children who were able to work for longer
periods would work for about 15 minutes and then have a 5-minute play activity at the end of
the session.
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115
Recruitment, Randomization and Blinding Procedure
Twenty four children enrolled in the elementary department of the school were
identified by their class teacher as likely to benefit from an individualized numeracy
intervention. Parents of the children were sent a letter informing them about the aims of the
study and about our intention to randomly allocate children into the intervention and control
groups. The study information sheet explained that children in the control group would also
receive Maths Recovery intervention during the following school year from the teaching staff
who would have been trained by the research team during the course of the current project.
All parents consented to their child’s participation in the study. A randomization protocol was
created for the needs of the study by the collaborating clinical trials unit (Appendix 9). The
children attended five different classes within the school, and it was important for practical
reasons to have balanced numbers of students who received one-to-one instruction in each
class. This was because the intervention would be delivered by the teaching assistants within
each class, something that would affect the staff-to-children ratio within classes. Therefore
two randomization criteria were used: the class the children were enrolled in, and their main
diagnosis (severe ID or ASD).
Once parents’ consent had been secured, the 24 children were pre-tested on the
standardized measures described in the next section. Children’s information was then entered
into the randomization template and emailed to the trails unit. Using block randomization, the
24 children were allocated into the intervention and control groups with twelve in each group
(ratio 1:1) and the results were emailed to us on the next working day. A consort style
diagram summarizing the design is presented in Figure 5.1. After the end of the intervention
period (4 months post-randomization), all 24 children were again tested on the same
standardized measures. Persons who were not otherwise involved with the study
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Recruited: n =24
Pre-tested: n=24
Allocated to Maths Recovery group: n=12
Received individualized teaching for 12
weeks: n=12
Allocated to control group n=12
Received “mathematics as usual”
teaching for 12 weeks: n=12
Post-testing at 4 months after
randomization: n=12
Analysis of pre- post- intervention scores:
n=11
Excluded from analysis (testing
difficulties): n=1
Post-testing at 4 months after
randomization: n=12
Analysis of pre- post- intervention
scores: n=11
Excluded from analysis (testing
difficulties): n=1
Follow-up
Allocation
Randomized n=24
Analysis
Recruitment
Figure 5.1: Consort style diagram
Follow up at 12 months after
randomization: n=11
Analysis of pre-post - follow up scores:
n=11
conducted all testing sessions, and so testers were blind as to which group the child belonged.
For 23% of testing sessions, a second assessor scored the child’s performance. Using the
percentage agreement index method, inter-rater agreement on the child’s scores was 99.7%
(range 97-100%). Two participants with a diagnosis of autism, one from each group, were not
cooperative during testing and we were unable to use their data. Therefore, results for 22
children, 11 in each group, were used in the final analysis.
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117
To assess whether the post-intervention gains had been maintained a follow–up test
on one of the standardized measures was conducted with the children in the Maths Recovery
intervention group only approximately 12 months after randomization.
Measures
Two main outcome measures were used in the present study:
The Test of Early Mathematics Ability 3rd edition (TEMA-3, Ginsburg & Baroody,
2003), is a standardized test designed to measure mathematical ability in typically developing
children aged between 3 years 0 months and 8 years 11 months, which can also be used with
older children with mathematical learning difficulties. The test includes a variety of
numeracy tasks, such as verbal counting, counting items, reading and writing numbers,
saying the number that comes after a given number, and story problems involving
additions/subtractions. The TEMA-3 has two parallel forms, A and B. Each of the 24 children
was tested with the same Form (some with A and some with B) at two time points: before
intervention, and at the end of the intervention period. For the children in the intervention
group, an additional follow up test (using the same Form as in the previous two tests) was
administered seven months after post-testing (12 months post-randomization). The test –
retest reliability for Forms A and B are .82 and .93 respectively (Ginsburg & Baroody, 2003).
TEMA-3 yields a raw score, a Math Ability score and an Age Equivalent (mathematical age)
score. Because the test has been designed for typically developing children up to the age of 8
years 11 months, Math Ability standard scores cannot be calculated for older students. As the
age range of our children was up to 11 years 2 months, we were able to use only the raw and
age equivalent scores for this test.
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118
The Early Numeracy Curriculum-Based Measurement (EN - CBM, Clarke & Shinn,
2002; Clarke et al., 2008) consists of four subtests, which are timed and last for one minute
each:
1. Oral Counting (OC): the student counts from one up to as high as he can go.
2. Number Identification (NI): numerals are presented in random order and the student
identifies them.
3. Quantity Discrimination (QD): the student needs to identify the larger number from a set of
two.
4. Missing Number (MN): the student is required to identify a missing number from a
sequence of three consecutive numbers.
As for our previous study with children with autism (described in Chapter 3), a small
adaptation was made to the format of NI, QD, and MN. Instead of presenting the child with a
page containing boxes with all test items, we printed each item on a card and presented one
item at a time. This was done to help avoid the possibility of confusion if the students were
presented with too many items at once. Participants of both groups were tested on the ENCBM subtests twice, at the beginning, and at the end of the intervention period.
Results
Results for the TEMA-3 test and the Oral Counting (OC) and Number Identification
(NI) subtests of the EN-CBM are summarized in Table 5.3. Because there were differences
between the mean scores of the two groups at pre-intervention, we conducted ANCOVA
analyses to evaluate the effects of the Maths Recovery intervention. We compared the postintervention scores of the two groups while controlling for pre-intervention scores. The
results indicated that the intervention group made significant gains on the TEMA-3 at post-
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119
test in comparison to the control group. On the EN-CBM test results there was a small
difference in favour of the intervention group on the OC subtest and no statistically
significant difference on the NI subtest. The OC results of one child in the Maths Recovery
intervention group were not included in analysis. This child had scores of 10 at pre-testing
and 65 at post-testing. However, as indicated by his TEMA-3 scores and his general
performance during the intervention period, the low pre-intervention score was likely due to a
lack of confidence rather than to his inability to count above 10. Therefore, this child’s score
was judged to be an outlying data point.
As for the remaining two subtests of the EN-CBM, Quantity Discrimination (QD) and
Missing Number (MN), many of the 22 children were unable to access them either at pre- or
at post-intervention. Five children in the intervention group and seven in the control group
were able to complete QD, whereas MN was accessed by six children in the intervention and
seven in the control group. The children in the Maths Recovery group who were able to score
on the subtests showed improvement in scores at post-treatment time: QD pre-test Mean =
9.00 (SD = 8.48), post-test Mean = 9.80 (SD = 7.15), and MN pre-test Mean = 6.33 (SD =
6.25), post-test Mean = 11.17 (SD = 10.08). The control group had a small decrease in the
two subtests: QD pre-test Mean = 11.14 (SD = 5.92), post-test Mean = 9.43 (SD = 3.95) and
MN pre-test Mean = 4.57 (SD = 6.21), post-test Mean = 3.71 (SD = 2.28).
Effect sizes (Cohen’s d) for the intervention effect were calculated using the method
recommended by Morris (2008). The mean pre-post difference for the Maths Recovery
intervention group minus the pre-post difference of the control group was divided by the
pooled pre-test standard deviation. Effect sizes were moderate for the TEMA-3 scores and
small for the OC subtest.
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120
Table 5.3
Pre-, post intervention and follow-up scores for the intervention and control groups
MR Intervention Group
(n=11)
Pre-test Post-test Follow -up
Control Group
(n=11)
Pre-test Post-test
ANCOVA
M (SD)
M (SD)
M (SD)
M (SD)
F
p
ΤΕΜΑ-3 raw
7.18
13.82
14.27
10.27
10.27
31.7
<.00
score
(9.54)
(11.83)
(13.65)
(9.66)
(9.36)
4
1
TEMA-3 math
43.36
51.55
52.64
48.27
48.55
17.9
<.00
ageª
(11.72)
(14.18)
(15.72)
(11.42)
(11.21)
3
1
Oral
13.10
17.70
-
15.00
15.00
3.42
.081
.43
Counting
(11.21)
(11.71)
(9.33)
(11.29)
Number
13.18
15.64
12.55
13.55
0.31
.583
.11
(12.25)
(12.15)
(12.72)
(14.62)
Identification
M(SD)
-
Cohen’s
d
.67
.66
Note. ANCOVA analyses and Cohen’s d have been calculated for the pre- post- test data only.
ªMaths age in months.
Because the number of children with an ASD diagnosis was not balanced across the
two groups and ASD participants in the Maths Recovery group had high post-intervention
scores, we run the analyses again excluding data of children with ASD across the two groups.
We found that the pattern of results remained unchanged.
Additional analyses were conducted to assess whether post-test scores of the Maths
Recovery intervention group were impacted by the person delivering the intervention. Results
indicated there was no such impact.
Children in the Maths Recovery intervention group had an additional follow-up test
on the TEMA-3 approximately 7 months after the end of the intervention (12 months postrandomization). These follow-up mean scores showed a slight increase compared to postintervention (see Table 5.3). Repeated measures t tests revealed that there were no
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121
statistically significant changes between post-testing and follow-up for Raw Scores (t (10) =
0.63, p = .541) or for Age Equivalent scores (t (10) = 1.00, p = .341) on the TEMA-3. Thus,
there was evidence of maintenance of the intervention effects over time.
Analysis of change at the individual child level
To evaluate change for individual children, we conducted an analysis of reliable
change (Reliable Change Index - RCI, Jackobson & Truax, 1991). The RCI focuses on the
amount of pre to post-intervention change necessary for the gains to be considered
meaningful and unlikely to have occurred by chance. Figure 5.2 shows the results of the
reliable change analysis on the TEMA-3 and the OC and NI EN-CBM subtests. Nine of the
11 children in the intervention group improved their mathematical age at post-test (range
between 3 and 18 months) and eight of them achieved reliable change. Two of the control
group children showed 3 months of mathematical age improvement and another child had a
3-month decrease. None of the children in the control group reached a reliable change level.
On the OC test, children in the intervention group generally made larger gains than the
control group children but only one child in each group achieved an increase above the
reliable change level. Data from one of the intervention group children was excluded from
this analysis because the score was an outlier. Finally, NI results show greater individual
variability, and none of the children reached a reliable change level.
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122
Figure 5.2: RCI results. Bars represent the change of individual children’s scores between pre
and post-intervention testing. The dotted lines indicate the change required to exceed the
reliable change index criterion. Top row graphs show the TEMA-3 raw scores and math age
scores. OC and NI scores of the EN-CBM test are shown in the bottom row graphs.
Chapter 5
20
14
15
4
5
1
5
6
3
2
0 0 0 0 0
1 1
0
-2 -2
9 9
-1
6 6
5
3
3 3
0 0
0 0 0 0 0 0 0 0
0
-3
Participants
-5
Participants
Maths Recovery
Intervention Group
20
Control Group
17
15
10
8 8
10
9
4
5
0
1
3 3
2
0 0
0
-5
-10
-2
-1
-1 -1
-3
-7
-8
Participants
4
NI Change - Numbers per Minute
OC Change - Numbers per minute
20
15
12 12
10
7 7 7
-5
Control Group
15
10 10
10
18
Maths Recovery
Intervention Group
Control Group
Maths Recovery
Intervention Group
Math Age Change in Months
20
Raw Score Change
123
Maths Recovery
intervention Group
15
8
10
Control Group
10 11
10 10
4 4 5
5
5
0 0 0 0 1
0 0
0
-5
-10
-2 -1
-3 -3
-9
-15 -12
Participants
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124
Discussion
The overall study outcomes were positive. The intervention group made a significant
gain on the TEMA-3, which covers a wide range of numeracy skills across different levels of
ability and therefore is the most comprehensive of the two tests we used. After 12 weeks of
individualized teaching, the Maths Recovery group improved their mathematical age by an
average of 8.18 months whereas the control group made an improvement of .27 months on
average. Focusing on individual participants, eight children (73%) of the Maths Recovery
group made a gain of at least 6 months of mathematical age, something that none of the
control group children achieved. Scores of two children in the Maths Recovery group
remained unchanged after the intervention. For the specific skills measured by the EN-CBM
test, which is a fluency-based measure (number of correct answers per minute), although the
intervention group made generally better progress than the control group the differences were
not statistically significant. Moderate effect size differences for OC and small for NI of the
EN-CBM were found at post-test in favour of the Maths Recovery group.
Another encouraging outcome is that the gains that the intervention group made at
post-test were maintained seven months after the end of the intervention period, demonstrated
by the follow-up test on the TEMA-3.
An important methodological strength of the present study was the random allocation
of participants into the two groups and testing at pre and post-test blind to intervention group
status. Employing this design in an applied setting such as a special needs school was made
possible by the support of school personnel and the children’s parents who were highly
interested in our investigation of a numeracy curriculum. No parent objected to their child’s
participation in the project even though it was understood that only half of the children would
be receiving intervention during the research period. The headteacher of the school welcomed
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our suggestion to conduct the study, and teaching staff members were supportive and willing
to cooperate with us throughout the different stages of the project (e.g., by attending training
meetings, delivering the one-to-one teaching, recording data).
The present study also has a number of limitations. Adherence to the proposed level
of intervention intensity (3 to 4 sessions per week) was not possible. In a large special needs
school setting events such as school outings, staff training sessions, or a child in the
classroom requiring extra attention, often resulted in the teaching assistants being unable to
find the necessary time to implement the Maths Recovery intervention. As a consequence,
intervention intensity was varied across participants in the intervention group. We did explore
the correlation between the number of sessions a child had received and the improvement
he/she made at post-test. However, there was no meaningful association found. Factors other
than intensity may play an important role in the intervention outcome. For example, it is
possible that there were IQ level differences between the two groups of children. However,
we did not have any information on IQ or Adaptive Behaviour scores. Access to more
detailed information on participant characteristics might enable future studies to determine
which children are more likely to benefit from individualized intervention. The analysis of
individual child data demonstrated that the largest gains were made in the Maths Recovery
group by the children with ASD. The association between autism diagnosis and outcomes
requires further attention in future research.
A further limitation of the present study was that although diagnosis was one of the
randomization criteria, the number of children with ASD was not balanced across the
intervention and control groups by the end of the study. At the time of randomization, three
children with ASD were allocated to the Maths Recovery group and two to the control group.
During the course of the research, an additional child in the intervention group was diagnosed
with ASD. Furthermore, we had been given mistaken information by the school regarding
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another child’s diagnosis at the beginning of the study. This child, also allocated to the Maths
Recovery group, actually had an ASD diagnosis. At the time of analysis, and after the loss of
one child with ASD from each group due to testing difficulties, there were four children with
ASD in the intervention group and only one in the control group. As reported above, we
conducted an analysis of the data excluding the children with autism and the differences
between the groups on the TEMA-3 test remained statistically significant in favour of the
intervention group.
We also did not assess treatment fidelity across the different members of staff who
delivered the intervention. Due mainly to the fact that the first author was herself daily
involved with teaching, the times when a teaching assistant was observed during a session
were limited to instances when a problem was reported with a specific child. The fact that
teaching staff in special needs schools are not familiar with ABA teaching methodologies
increases the possibility of inconsistency in the quality of intervention delivery. For future
studies, especially if the intervention is to be implemented with larger numbers of
participants, a higher level of support, supervision and fidelity checks will be needed.
Despite the limitations, we believe that the present study contributes to the existing
body of research on mathematics interventions with children with severe ID and has some
important implications for researchers and practitioners working in this area. We have
demonstrated that it is possible to conduct studies with strong experimental control such as
randomized controlled trials, within applied educational settings. Implementation of an
individualized intervention in a non-ABA context and without the use of additional funding
resources also proved feasible. However, this was partly due to the relatively small number of
children who received the intervention. For future, larger scale intervention implementation,
additional resources would be needed. We would recommend that one member of teaching
staff in the school receives relevant training and is given the necessary time to serve as a
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127
consultant for the program, taking on tasks such as: providing training and supervision to
other members of staff, troubleshooting individual children’s programs, and creating and
organizing teaching materials .
Outcomes of the present study support previous research findings regarding the
importance of systematic instruction when teaching mathematical skills to children with
severe ID (Browder et al., 2008). We used a highly structured teaching approach which
included specified and measurable goals, systematic use of prompting and prompt-fading
procedures, generalization training, and data collection in every session. Furthermore, the
Maths Recovery curriculum is well structured and systematic with numeracy targets
organized both horizontally (different groups of activities within the same ability level – key
topics) and vertically (progressive stages of difficulty). We suggest that both the teaching
methodology and the curriculum content need to be well structured for a mathematics
intervention to be effective.
In their discussion document on the development and evaluation of complex
interventions (MRC, 2008), the Medical Research Council suggest a sequence of stages: (a)
identification of the intervention components, (b) an exploratory phase of one or more pilot
trials, (c) definitive evaluation employing study designs with appropriate statistical power,
(preferably a randomized controlled trial - RCT), and (d) long-term implementation in a nonresearch environment. In line with this model, we identified Maths Recovery as an early
numeracy curriculum that could potentially be used with children with developmental
disabilities, and we then conducted a small pilot study with six children with autism in an
ABA setting (Chapter 3) which yielded positive results. The present pilot RCT provides some
evidence that the adapted Maths Recovery numeracy curriculum can be effective leading to
meaningful improvements in the skills of children with ID. We also tested procedural
components that would be needed in a definitive RCT (e.g., randomization, teaching
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procedures, outcome measures, longer term follow-up). However, the intervention was
implemented over a relatively short period, with a limited range of outcome measures (e.g.,
we did not test impact on functional day-to-day numeracy skills), without an alternative
mathematics curriculum as a comparison intervention, and without measures of intervention
integrity. Thus, further RCT studies are needed to develop the evidence base for the Maths
Recovery intervention with this population.
Chapter 6
Chapter 6: General Discussion
129
Chapter 6
130
The present thesis has attempted to expand existing knowledge on effective schoolbased educational practices for children with autism spectrum disorder (ASD) and/or
intellectual disability (ID). Two main areas have been explored: (a) the development of social
skills, and (b) the formulation of appropriate curricula and teaching methodologies to teach
academics to these children. Effective strategies and materials for both of these important
areas of education are very much needed (Strain & Schwartz, 2001).
Within the domain of social skills, an area that has been suggested might play a
pivotal role in the overall development of children with ASD was targeted in the two
empirical studies that comprise Chapter 2: verbal initiations towards peers. The approach we
investigated, the use of a tactile prompting device that cued the child with autism to approach
a peer and verbally initiate, had previously been used in two published studies (Shabani et al.,
2002; Taylor & Levin, 1998). The present thesis successfully replicated and further refined
this method by introducing a more systematic training phase and incorporating the use of
prosthetic reinforcement throughout the intervention period. More importantly, we
successfully faded the use of all additions to the environment, by gradually removing first the
tactile prompt and then the prosthetic reinforcement while maintaining a high rate of verbal
initiations.
The next three chapters of the present thesis explored the area of teaching academics,
and more specifically, mathematical skills to students with ASD or ID. Chapter 3 of this
thesis was concerned with a systematic exploration of the existing literature on mathematical
interventions with children with ASD. Sixteen relevant studies were located. Only six of
these studies were specifically designed to teach one or more mathematical skills to students
with ASD. The remaining 10 studies either included students without autism (typically
developing or with a different diagnosis) or targeted non-mathematical as well as
mathematical skills. Each of these two categories was reviewed separately. The majority of
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131
the studies reported positive findings for the students with ASD. The methodological strength
of the reviewed studies was measured based on the Scientific Merit Rating Scale (National
Autism Center, 2009). Of the different mathematical interventions evaluated in the reviewed
studies only one was used in three different projects, the use of touch-points to teach addition
and subtraction skills. All three studies had a good level of methodological quality and
reported positive results. Therefore this intervention can be deemed as exceeding the
emerging stage of evidence although it still needs additional evidence before it can be
characterised as established (National Autism Center, 2009). This systematic review found
that certain mathematical areas (e.g., geometry, data analysis) have not been targeted in
published research. Another conclusion was that there is a shortage of comprehensive
mathematical curriculums for use with children with autism; interventions described in the
included studies targeted one or two isolated mathematical skills.
In Chapter 4 Maths Recovery, a numeracy curriculum originally designed for
typically developing children who were performing below the age-appropriate level in
mathematics (Wright et al., 2006a), was adapted for use with children with ASD enrolled in
ABA programs. The adaptations targeted issues like the simplification of verbal instructions,
breaking complicated tasks into smaller steps, the inclusion of prompting and prompt- fading
strategies and the addition of a generalization step for each of the lessons. A pilot study was
then conducted in the Westwood ABA class with six children with ASD who received
individualised numeracy teaching with the adapted Maths Recovery curriculum. Pre- and
post- intervention tests revealed that after 20 weeks of intervention all six children improved
their numeracy scores.
In Chapter 5 a second evaluation study of the Maths Recovery curriculum was
presented. This was a pilot RCT study that included children with ID as well as ASD and was
conducted in a non-ABA environment. Twenty-four children with an ID or ASD diagnosis
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132
were randomly allocated into the intervention (Maths Recovery) and control (mathematics as
usual) groups. At the end of the 12-week intervention period comparisons of pre- and posttest scores of the two groups revealed significant differences in favour of the intervention
group on a standardized numeracy measure.
The two studies presented in Chapters 4 and 5 of the present thesis are the first
projects to have evaluated the Maths Recovery curriculum with children with intellectual and
developmental disabilities; (all previously published research has been conducted with
typically developing children). They are also among the first studies that have evaluated a
comprehensive mathematical curriculum with this population.
An important element of the present thesis is that both the social skills and the
mathematical intervention studies were conducted across different types of educational
settings. Study 1 of the tactile prompt project was conducted in the Westwood ABA class
whereas in Study 2 the intervention phases with the two participants were conducted in a
mainstream school and an Out-of-school-club respectively, and the training phase during
home ABA sessions. The Maths Recovery studies were conducted in the Westwood ABA
class and in a special needs school that served children with ASD and/or ID. This was to
some extend the result of a change of circumstances rather than the original plan at the
beginning of the research project. However, the fact that the interventions described in the
present thesis were shown to be effective not only in a school setting with a high staff-tostudents ratio but also across different school environments is an important finding. Children
with ASD/ID are being educated in diverse educational settings worldwide, often under less
than optimal conditions and for research to be relevant to practitioners interventions need to
be tested in “real world” settings.
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133
Methodological limitations of the current research
The research projects included in the present thesis have added to the existing
knowledge on educational practices for children with ASD and/or ID; they do however have
a number of weaknesses.
In the Maths Recovery study conducted in the Westwood ABA class an A-B design
was used; this was not a strong methodological design. Using a quasi-experimental control
group design, with children enrolled in another ABA school setting participating in the
control group would have allowed for a higher methodological quality; however this did not
prove possible in practice.
Another weakness of the same study is the very small percentage of teaching sessions
(5%) that we were able to collect treatment fidelity data. This was partly due to the fact that
unlike group teaching formats – whether in regular education or in special education classeswithin ABA-based programs the therapist does not use a set timetable for the different areas
he/she teaches (e.g., English: 9.00-10.00; Mathematics: 11.00-11.45). Instead, the pupil
works on tasks from each area (e.g., language, academic skills, play skills) for short periods
throughout the day; working on mathematics was therefore conducted during short sessions
(e.g., 5 minutes at a time) throughout the whole school day. This meant that it was not easy to
arrange observations.
The Maths Recovery RCT study (Chapter 5) was also weak in this area as we were
unable to collect any treatment fidelity data. In the special needs school environment where
this study was conducted, apart from the issue of the teaching timetable which was not stable
(i.e., the teaching assistants often had to vary the time they taught the children with Maths
Recovery due to various classroom issues), an additional difficulty was the shortage of
available time for supervision purposes. I was the only person who had the necessary
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134
expertise to supervise the teaching assistants, and the majority of my time was taken up by
delivering individualised teaching to pupils. Consequently the amount of time I was able to
devote to supervisory work was limited. According to the Scientific Merit Rating Scale
(National Autism Center, 2009) we used to evaluate methodological strength in the studies
we reviewed in Chapter 4, treatment fidelity should be measured for 25% of sessions at a
percentage exceeding 80% for the study to be given a score of 5 (indicating strong scientific
merit). This is therefore an important area that should be addressed in future research.
Videoing teaching sessions could possibly help future researchers to overcome difficulties in
this area.
Another limitation of the RCT study involves the fact that we were unable to use the
standard score of the main standardized test (TEMA-3, Ginsburg & Baroody, 2003), the Math
Ability score. The test has been standardized for typically developing children aged 3 years to
8 years 11 months; many of our participants were of an older chronological age and the Math
Ability score could not be calculated for them. We used therefore only the raw scores and the
Age Equivalent (mathematical age) scores the TEMA-3 yields. Ginsburg and Baroody (2003)
advice that some caution should be exercised when using the mathematical age scores.
Despite this limitation and in the absence of any standardized mathematical tests specifically
designed for children with intellectual and developmental disabilities, we found this test to be
the most appropriate as it is a detailed numeracy skills test that can be used with children
across different levels of abilities.
Additional limitations of the RCT study were the relatively short duration of the
intervention period (12 weeks), the fact that intensity of intervention varied across children of
the Maths Recovery group, and the unequal numbers of children with ASD and ID across the
intervention and control groups.
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135
Implications for future research
In this section we will consider ways that the two main areas investigated in the
present research, (a) the use of a tactile prompt to increase the verbal initiations of children
with autism towards their peers, and (b) the evaluation of the adapted Maths Recovery
curriculum with children with ASD and/or ID, can be extended in the future.
A. Social interventions for children with autism
The present evidence base for the use of the tactile prompt to increase the rate of
verbal initiations of children with ASD during free-play activities with typically developing
peers has been strengthened by the findings of this thesis. Four studies in total have reported
positive findings with all 9 participants. These are promising results of a relatively simple,
unobtrusive and easy to implement prompting method. Within the complex area of social
interactions however, there is still a number of issues that need further investigation. In
regards to this particular intervention, an important element that needs to be examined is its
longitudinal effectiveness. Considering the severity of the social skills impairments in
persons with ASD it is possible that with time the gains the children make with this
intervention might decrease. Future projects could include additional follow-up tests and
possibly implement additional intervention stages depending on the results. Another
important aspect that needs attention and can be examined in future research is the
generalization of the intervention effects across different environments and peer groups (e.g.,
the target child’s verbal initiations towards his/her siblings at home). As children with ASD
have generalization difficulties, it is possible that some additional training might be needed
for an increased rate of initiations across multiple social contexts.
Other findings of the present research, apart from the frequency of initiations, involve
the overall quality of the social interactions between the target children and their peers. The
Chapter 6
136
transcript data indicated that the target children’s quality of initiations improved during the
course of the intervention, however they were at times awkward. Additionally, the rate of
peers’ responses to the target children’s initiations was not high. These findings show the
serious underlying difficulties children with autism often have in the area of social
interactions and point towards the need for further improvement of interventions. Although
we taught the children a number of phrases they could use to initiate to their peers, the
primary aim of the tactile prompt intervention was to help increase the initiation rate and
therefore does not fully address all aspects of social interaction difficulties. Possibly in future
studies the tactile prompt intervention could be part of a social skills training “package”
which would include a more systematic teaching of reciprocal peer interactions and thus
better address the overall quality as well as the rate of interactions.
B. Mathematical interventions for children with ASD and/or ID
In regards to the evaluation of the adapted Maths Recovery curriculum for children
with ASD and/or ID, the two studies included in the present thesis have accomplished certain
of the stages defined by the MRC complex interventions framework (Medical Research
Council, 2008). Our results indicated that the program can be effectively used with both
groups of children (i.e., ASD and ID) and that it can be implemented in ABA and in nonABA environments. We have also provided some answers to questions related to other
procedural issues such as the possibility of conducting randomized trials within school
environments, the effectiveness of teaching procedures, and the resources needed for largerscale implementation.
There are still many issues that need to be addressed by future research. The present
data base is still small – 18 children in all have received individualized teaching with the
Chapter 6
137
adapted Maths Recovery curriculum in the two studies included in the present thesis.
Evaluation by larger scale studies is necessary.
The duration of our studies was relatively short – 20 and 12 weeks respectively. To
better evaluate the curriculum more longitudinal studies should be conducted; for example
evaluating the progress of the children after implementing the curriculum for a whole
academic year would probably allow for drawing firmer conclusions.
Another consideration is that the majority of the children treated so far were working
on tasks from the Emergent stage of Maths Recovery (e.g., numbers 1 - 20, numerals 1 – 10,
counting up to 20 items). Consequently some of the more advanced stages of the curriculum
such as the Counting-On stage (e.g., counting in 2s, 5s, 10s, numerals up 1000, adding and
subtracting by tens) and the Facile stage (e.g., counting by 10s and 100s, 2-digit additions and
subtractions, advanced multiplication and division) have not been evaluated in our studies.
Future projects could conduct separate analyses of the effectiveness of the program with
beginning, intermediate and advanced learners.
In the RCT study (Chapter 5) we compared the progress of children taught with Maths
Recovery to that of children who received “mathematics as usual” teaching. As the
information on the exact nature of what consists “mathematics as usual” is rather vague,
conducting future projects using a comparison group taught with a different mathematical
curriculum might lead to a more convincing argument in favour of Maths Recovery. Another
possible argument is that there is no way of assessing whether the post-intervention gains
should be attributed to the curriculum itself or to the individualized teaching. Studies that use
a comparison group that does receive individualized mathematical teaching (e.g., within an
ABA school setting) will provide convincing answers to this question.
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138
An additional direction for future evaluation studies on Maths Recovery is using more
homogenous groups of participants (i.e., with an ASD or ID diagnosis only, instead of mixed
groups), or have more balanced numbers of participants with each diagnosis within each
group.
Practical implications of the present research: applying acquired knowledge in
the context of a Greek special needs pre-school
In this section ways that the overall knowledge acquired throughout my studies – not
just the PhD research itself – can be applied in my current work setting will be examined. At
the time of the writing of this chapter I have been working for approximately one and a half
month in a special needs pre-school in the suburbs of Athens. Five children are enrolled in
my class: three of them are 6 years of age and have been diagnosed with different degrees of
intellectual disability; additionally, two of these children have language difficulties and the
third has behavioural problems. The remaining 2 children are 4 years old and have an ASD
diagnosis. They are both non-verbal and have very few skills. Generally the children come
from families with a low socio-economical background and with the exception of one child
with ASD they do not receive educational services (e.g., speech and language therapy)
outside of the pre-school.
The greatest challenge I face in my work in this setting involves the difficulty of
allocating individualised time to each of the children. In Greek special needs schools there
are usually 6 to 7 children per classroom. However, the number of teaching assistants
working in the schools is very small; in my school there are 2 teaching assistants in a school
with a total of 45 students (40 elementary school children and my 5 pre-school children).
Consequently, for the majority of the school day the teacher is the only adult in the class. In
these circumstances it is possible to work individually with each child for only short intervals
Chapter 6
139
(e.g., 10 – 15 minutes at a time). Therefore I am incorporating the basic elements of the
behavioural model of education described in Chapter 1 (i.e., skills assessment, task analysis,
reinforcement, prompting and prompt-fading procedures, functional analysis of problem
behaviours); however individualised teaching is conducted in a non-intensive format.
Skills assessments based on the ABLLS (Partington & Sundberg, 2006) are ongoing
with all the children in my class at this point. Certain teaching targets have been chosen for
each child based on the parts of the ABLLS that have been completed, as well as on
behavioural teaching manuals for children with ASD (Leaf & McEachin, 1999; Maurice et
al., 1996) and we are working daily on them. Individual programs vary; for one of the more
advanced children, language targets include the expressive identification of verbs/actions
using the correct grammatical form (i.e., use the forms of the verb that indicate
singular/plural). For example, the child is shown a picture of two people who are cooking and
is asked “what is happening?” The target is for her to say “they are cooking” as she often
makes mistakes and might say “he is cooking”. With another child who has good receptive
language skills (i.e., can identify at least 100 items, can identify verbs) but only uses a very
limited vocabulary of single words many of which are in a “baby language” form, we are
working on targets suggested by the speech and language therapist of the school to help him
with the production of the basic sounds and sound combinations. For one of the younger
children with ASD, initial targets include sitting on a chair for a few minutes, imitating
actions using items (play a drum, stack 3 blocks, stir a cup with a spoon), and self-help skills
(i.e., dressing skills).
Numeracy targets from the Maths Recovery curriculum have also been incorporated
in the individualised programs of two of the older children. Current individual targets include
verbal counting 1 to 5 (key topic 1), reading number-lines 1 to 3 (key topic 2) and counting
Chapter 6
140
collections of up to 5 items (key topic 3). Additionally, counting using fingers of one hand
(key topic 5) activities are being conducted during small-group sessions.
Systems of reinforcement are used with all the children. With the 3 older children I
am using token systems; when all the tokens have been collected the child exchanges them
with a preferred activity (e.g., a computer game, a musical toy). With the younger children
with ASD small food items (e.g., Cheerios®, raisins) and physical play (e.g. tickles) are
being used at this stage on a continuous schedule (FR 1 ratio).
An element of my PhD research that I find especially useful at this point in my
teaching job is the fact that the studies included in the present thesis were conducted in two
very different school environments: the ABA Westwood class and the special needs school.
The ABA class with the one-to-one staff to child ratio, high level of senior staff expertise,
program organisation and staff training was an ideal school environment for the young
children with ASD who received intensive individualised teaching (compared to other school
settings though less so than home programs) combined with opportunities for social
interaction with typically developing children and integration into regular education
environments. It was also an environment that offered excellent opportunities for applied
learning to practitioners such as myself. In the special needs school where the Maths
Recovery RCT study (Chapter 5) was conducted, where the staff-to-children ratio allowed for
limited opportunities for individualised teaching, I had an opportunity to put to practice ABA
techniques I had learned in the Westwood class. It was especially important that despite the
challenges and the limitations, it was possible to implement in that environment a program
that involved individualised teaching as the RCT study demonstrated. As the school I am
presently working has much in common with the special needs school in North Wales, the
positive results of the study conducted in that setting are an encouragement for me. As other
Chapter 6
special education teachers have discovered, “it is possible to incorporate ABA in any
classroom practice” (Grey, Honan, McClean, & Daly, 2005).
141
Chapter 6
Conclusions
In conclusion, the present thesis has demonstrated ways that Applied Behavioural
Analytic methodologies can be applied in various domains of the school education of
children with autism spectrum disorders and/or intellectual disabilities. An important
contribution of the current research is the demonstration that these methodologies can be
effectively applied across different educational contexts.
142
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143
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154
Appendices
155
Appendices
Appendices
156
Appendix 1
Information to participants (Chapter 2)
1a: Information sheet for parents
1b: Research consent form for parents
Appendices
157
Appendix 1a
Information Sheet for Parents
Study title
Use of a tactile prompt to increase social initiations in children with autism
Project team
Pagona Tzanakaki, Research student
MSc student, to be named
Richard Hastings, Professor of Psychology
Carl Hughes, PhD, BCBA, Course Director of ABA MSc
This research project is being carried out by Bangor University.
Purpose of the study
One of the difficulties associated with autism is the lack of interest in social interactions.
When children with autism find themselves in a group of other children, they often prefer to
play alone and usually do not approach their peers to make conversation or invite them to
play together. As a consequence, they experience much less interactive play and conversation
compared to their peers, something that can limit their social and verbal learning
opportunities. There is also the danger that they might face difficulties with socialization later
on in their lives. It is therefore important that behaviours such as taking the initiative to talk
to a peer or respond when the peer is talking to them be systematically taught at a young age.
Appendices
158
In this project we would like to see whether a small vibrating device can be successfully used
to help remind children with autism to talk to other children during free play time. The device
is small (about 2X2 inches) and can be placed in the child’s pocket, so other people around
your child will not be aware of it.
Procedures involved
To assess your child’s current level of talking to his peers, we will initially observe him
during play time with mainstream children; during this first phase the child will not be given
any directions on how to interact with his peers.
As a next step, the school personnel who work with your child in the ABA class, will teach
him to approach a peer and talk to him (e.g. invite him to play) every time the pager in his
pocket vibrates. During the training phase an adult will play the role of the peer.
Once the child is familiar with the vibrating pager, the device will be placed in the child’s
pocket during free play time with children from the mainstream part of the school. The
therapists who normally accompany your child in these activities will be with him and will
reward him with tokens if he approaches a peer and talks to him when the pager vibrates.
Tokens are usually stickers or little pictures that are attached with Velcro on a token board.
They will later be exchanged with activities that your child enjoys (e.g. he will be given a
choice of spending a few minutes on the computer, play station, soft play area etc).
After the child has learned to approach other children with the use of the pager, we will
remove the vibrating pager for a few days to observe how the child’s behaviour will change
as a result (e.g. we expect that talking to peers will be reduced) and we will then reintroduce
the vibrating pager. The purpose of this (removal-reintroduction of the device) is to ensure
Appendices
159
that any changes we see in the child’s behaviour are a result of the intervention and not of
some other factor.
During the final phase of the experiment we plan to start “fading” the frequency of the
vibrations slowly and the hope is that this will then help your child to initiate play activities
without the prompt.
Throughout all the phases described above sessions will take place 3-4 times per week, once
a day, and last 10 minutes each. During these sessions we will be observing your child and
taking data on his behaviour of taking the initiative to talk to another child or responding to
another’s initiation.
The expected duration of the whole procedure is about 3 months.
What are the benefits of taking part?
With this research project we hope to identify a simple method that will help to increase
children’s level of initiations to their peers. A benefit of the method is that it does not draw
attention to the child and does not make him stand out among other people around him.
Are there any risks involved?
We do not believe that the children participating in the study are being put in risk in any way.
As mentioned before, the vibrating device is small and it is unlikely that it will cause any
distress to the children. They will also have the chance to gradually get used to it in the
training sessions. Your child’s identity will be protected at all times and the completed study
will not include their name, the name of the school, or any other identifying information.
Appendices
160
Your participation is completely voluntary and you reserve the right to withdraw your child
from the study at any time without giving any explanations and without this affecting his/her
education in any way. If you have any further queries about the study please do not hesitate to
contact us, our details are below.
Pagona Tzanakaki
Postgraduate Research Student
The ABA Class
Westwood Primary School
Tabernacle Street
Buckley, Flintshire
CH7 2JT
Email: [email protected]
Tel: 01244 545731
Or, you may contact the supervisors directly:
Professor Richard Hastings/ Dr Carl Hughes
School of Psychology
Adeilad Brigantia
Penrallt Road
Gwynedd LL57 2AS
Email: [email protected], [email protected]
If you have any complaints about how this study is conducted please address these to:
Professor Oliver Turnbull
Head of School of Psychology
Bangor University
Gwynedd
LL57 2DG
Appendices
161
Appendix 1b
Research Consent Form for Parents
Please complete the following and circle as necessary:
1. Have you read the information on the Information sheet?
YES / NO
Have you had an opportunity to ask questions and discuss this study?
YES / NO
Have you received satisfactory answers to all your questions?
YES / NO
2. Do you give consent for your child to participate in the study?
YES / NO
3. Are you aware that you can withdraw your child from the study at any time without
giving a reason for withdrawing?
4. Would you like a copy of this consent form?
YES / NO
YES / NO
5. Would you like to be sent a copy of the study or, if it is published, a copy of the
printed article?
YES / NO
Signature______________________________________________________________
Date__________________________________________________________________
Your name ____________________________________________________________
Your child’s name ______________________________________________________
Address_______________________________________________________________
______________________________________________________________________
____________________________Postcode__________________________________
Please return this form, at your earlier convenience, to Pagona Tzanakaki at the ABA Class in Westwood
School.
Appendices
162
Appendix 2
Manual for the training phase of the tactile prompt project
Teaching Plan Familiarization with tactile
prompting devise (motivaider)
Stage one
Medium Term Objective: Child will not show any visible signs of distress when a
vibrating motivaider devise vibrates in their pocket
Materials: Motivaider, child’s file, data sheets, reinforcers
Teaching Procedure:
Frequency of training
If the child is immediately not distressed by the motivaider (i.e., they probe correct at the
highest vibration setting with their hand on top of the motivaider on the table and then
with the motivaider being in their pocket) then move straight away onto Stage Two. If
needed, and the child is initially distressed, conduct at least two training sessions a day,
each lasting approximately 5 minutes, and follow the procedure below:
1. Determine reinforcement
Ask the child what they would like to exchange their tokens for at the end of the session
(in keeping with how you usually do in your session). Use stimulus preference
assessments if necessary.
2. Set the device- Set the vibrating devise to buzz at 30 second intervals (VI schedule).
Initially start with the highest vibration setting
SD1: “Lets practice using this buzzer, it will buzz every now and then” (put on table and
child’s hand on top of it) and set to vibrate at VI 30 sec intervals). “See it vibrates and
makes a buzzing noise”.
SD2: Lets practice using this buzzer now in your pocket (put in child’s pocket with child’s
hand on top).
SD3: Now lets put it in your pocket (put in child’s pocket, hand out of pocket).
For each step reinforce the child for tolerating the vibration (even if they are initially
agitated). By pairing the sensation with reinforcement the vibration will become less
aversive to them. Gradually fade this procedure so you reinforce with tokens only those
trials where the child remains calm.
Prompting Suggestions:
(1) If the child appears distressed with the motivaider initially set to the highest
setting, adjust the setting on the motivaider to the lowest setting. There are five
settings which gradually increase the strength of the vibration. Work through the
different settings
(2) If the child appears distressed model that it is ok, and provide reassuring
comments (e.g., “See it doesn’t hurt, it just buzzes a bit. Now, you have a turn”)
(3) Have favourite toy characters hold the motivaider and provide similar reassuring
comments. Then provide child with opportunity to have a turn.
Appendices
Data Collection:
On the trial by trial data sheet:
Correct Response: Shows no response or no adverse reaction to the motivaider
Incorrect Response: Appears distressed or upset by the motivaider devise (e.g., quickly
takes hand off when it vibrates, pushes/ throws the devise away, mands for it to be taken
away- “Stop it”, “I don’t like it”, etc)
On the skills tracking sheet: Record the date each target was introduced and mastered.
Mastery Criterion: Using trial by trial data, two consecutive trials for each stage (i.e.,
buzzer on table child’s hand on top, buzzer in pocket, etc) with no visible signs of
distress.
163
Appendices
164
Teaching Plan Motivaider on table- child’s hand
on top
Stage Two
Medium Term Objective: With rule card on the table in front of they child, they will ask
a different question each time the devise vibrates when the motivaider is on the table
and their hand is placed on top
Materials: Motivaider, child’s file, data sheets, rule cards, tokens and token board,
reinforcers
Frequency of training: Conduct two training sessions a day, each lasting approximately
10 minutes. This could be broken up into smaller segments if required. You should aim
to do at least 20 trials each day. If the child masters this stage in one session, introduce
the next stage in the same day. Try to get through the training stages as quickly as
possible. This may mean that you master a few stages in one day
Teaching Procedure
1. Determine reinforcement
Ask the child what they would like to exchange their tokens for at the end of the session
(in keeping with how you usually do in your session). Use stimulus preference
assessments if necessary.
2. Set the device
Set the vibrating devise to buzz at 30 second intervals (FI schedule). This should give
enough time to prompt and provide quick reinforcement. If not, discuss with Corinna,
Pagona or Maria to adjust the time settings.
3. Child reads rule card
SD1: “Today you will be practicing with me how you can ask your friends questions”
(Hand child a rule card). “Let’s read what it says on this card”
I can get tokens for asking my friends questions. I can say:
Where do you live?
When’s your birthday?
Can I play with you?
Do you have any pets?
What’s
favourite
programme?
R1: Child should
read your
the card,
but TV
help
with any words that he finds difficult.
Appendices
4. Child asks questions when cued by the buzzer
Immediately after the child has read the questions on the rule card use most-to-least
prompting procedures to teach the child how to ask the questions when cued by the
buzzer.
Step one: Prompted trials
SD1: “Lets practice now using the buzzer and asking these questions”. (Put the buzzer
on the table in front of the child and place the child’s hand on top of the buzzer). “Each
time you ask me a question from the card I will give you a token”
SD2: When the buzzer vibrates, say “Ask me a question” and simultaneously point to a
question on the rule card. Each time you point, point to a different question on the card.
R: Child asks question on the card
C: Nice asking (and give a token), and then provide a quick response to each child’s
question (Thus, if they say, “Can I play with you?” say “yes, Lets play the tickling game”
and give them a quick tickle. Always choose an activity that means that the child can
stay sitting down at the table).
If they have asked a social question (e.g., when’s your birthday?”), sometimes answer
and then repeat the question (i.e., reciprocal social questions), however you are not
taking data on this and they do not have to respond (although it would be nice if they
did!).
Every five trials present a different rule card that has the questions written on in a
different order. Thus, if the child immediately asks all questions correctly and masters
the stage then there is no need for a new rule card. However, if they make some errors
and need more than five trials to master a stage then you would need to rotate the cards
so they see the questions in a different order every five trials.
Step two: Unprompted trials
Keep rule card on the table in front of the child
Fade ‘ask me a question’ prompts first, followed by pointing prompts, and only provide
tokens for unprompted trials. If additional prompts are needed you could “jiggle” the card
to draw their attention to it, but this also needs to be faded as soon as possible.
Continue, as above until child asks a different question unprompted for five consecutive
trials.
Data Collection:
On the trial by trial data sheet:
Correct Response: Says a different question on the rule card on consecutive trials
clearly so that it can be understood. Says a socially appropriate question that is not on
the rule card.
Incorrect Response: No response within 3 seconds of vibration; Gives an inappropriate
statement or question (e.g., verbal stereotypy; swearing); speaks unclearly so that the
question cannot be understood; says the same question on consecutive trials (if they say
the same question two or three trials later this is acceptable). Indicate the error made in
the margin (NR- no response; IQ- Inappropriate question; US- Unclear speech; Rpt-
165
Appendices
Repeated question)
On the skills tracking sheet: Record the date each target was introduced and mastered.
Prompting Suggestions:
(1) Use prompts, as described above, when you first introduce this program
(2) For inappropriate questions- therapist should model an appropriate question
(3) For unclear speech- therapist should say, “Say it clearly” and present an echoic
trial (e.g., “Say, What’s your name?”).
(4) For saying the same question on consecutive trials- therapist, should say, “You
need to ask a different question (and point to a different question on the rule
card)”
Mastery Criterion: Using trial by trial data, five consecutive correct trials with no
prompts
166
Appendices
167
Teaching Plan Motivaider in pocket- child’s hand
Stage Three on top
Medium Term Objective: With rule card on the table in front of they child, they will ask
a different question each time the devise vibrates when the motivaider is in their pocket
and their hand is placed on top
Materials: Motivaider, child’s file, data sheets, rule cards, tokens and token board,
reinforcers
Frequency of training: Conduct two training sessions a day, each lasting approximately
10 minutes. This could be broken up into smaller segments if required. You should aim
to do at least 20 trials each day. If the child masters this stage in one session, introduce
the next stage in the same day. Try to get through the training stages as quickly as
possible. This may mean that you master a few stages in one day
Teaching Procedure
1. Determine reinforcement
Ask the child what they would like to exchange their tokens for at the end of the session
(in keeping with how you usually do in your session). Use stimulus preference
assessments if necessary.
2. Set the device
Set the vibrating devise to buzz at 30 second intervals (FI schedule). This should give
enough time to prompt and provide quick reinforcement. If not, discuss with Corinna,
Pagona or Maria to adjust the time settings.
3. Child reads rule card
SD1: “Today you will be practicing with me how you can ask your friends questions”
(Hand child a rule card). “Let’s read what it says on this card”
I can get tokens for asking my friends questions. I can say:
Where do you live?
When’s your birthday?
Can I play with you?
Do you have any pets?
What’s
favourite
programme?
R1: Child should
read your
the card,
but TV
help
with any words that he finds difficult.
Appendices
4. Child asks questions when cued by the buzzer
Step one: Unprompted trials
Because of the high levels of prompting in the previous phase of teaching. You will start
this training phase with no prompts, but then use prompts if needed following the least to
most prompting procedure (see prompting suggestions below).
SD1: “Lets practice now using the buzzer and asking these questions”. (Put the buzzer
in the child pocket and place the child’s hand on top of the buzzer). “Each time you ask
me a question from the card I will give you a token”
So that you know when the buzzer has vibrated in the child’s pocket start a timer at the
same time as the buzzer. Every 30 seconds you would know to prompt the child if no
question was forthcoming.
R1: When the buzzer vibrates, child asks question on the card
C: Nice asking (and give a token), and then provide a quick response to each child’s
question (Thus, if they say, “Can I play with you?” say “yes, Lets play the tickling game”
and give them a quick tickle- choose an activity that means that the child can stay sitting
down at the table).
If they have asked a social question (e.g., what’s your name?”), sometimes answer and
then repeat the question (i.e., reciprocal social questions), however you are not taking
data on this and they do not have to respond (although it would be nice if they did!).
Every five trials present a different rule card that has the questions written on in a
different order. Thus, if the child immediately asks all questions correctly and masters
the stage then there is no need for a new rule card. However, if they make some errors
and need more than five trials to master a stage then you would need to rotate the cards
so they see the questions in a different order every five trials.
Prompting Suggestions:
(1) Use least to most prompts, as described in Stage two (e.g., if ‘jiggling’ the card
to bring their attention to it doesn’t work, then point to a question on the card, if
this also doesn’t work then also use a verbal cue “You need to ask me a
question”, at the same time as pointing.
(2) For inappropriate questions- therapist should model an appropriate question
For unclear speech- therapist should say, “Say it clearly” and present an echoic trial
(e.g., “Say, What’s your name?”).
(3) For saying the same question on consecutive trials- therapist, should say, “You
need to ask a different question (and point to a different question on the rule
card)”
Data Collection:
On the trial by trial data sheet:
Correct Response: Says a different question on the rule card on consecutive trials
clearly so that it can be understood. Says a socially appropriate question that is not on
the rule card.
168
Appendices
Incorrect Response: No response within 3 seconds of vibration; Gives an inappropriate
statement or question (e.g., verbal stereotypy; swearing); speaks unclearly so that the
question cannot be understood; saying the same question on consecutive trials (if they
say the same question two or three trials later this is acceptable). Indicate the error
made in the margin (NR- no response; IQ- Inappropriate question; US- Unclear speech;
Rpt- Repeated question)
On the skills tracking sheet: Record the date each target was introduced and mastered.
Mastery Criterion: Using trial by trial data, five consecutive correct trials with no
prompts
169
Appendices
170
Teaching Plan Motivaider in child’s pocketStage Four child’s hands on table
Medium Term Objective: With rule card on the table in front of they child, they will ask
a different question each time the devise vibrates when the motivaider is in their pocket
and their hand is not in their pocket (i.e., is on the table).
Materials: Motivaider, child’s file, data sheets, rule cards, tokens and token board,
reinforcers
Frequency of training: Conduct two training sessions a day, each lasting approximately
10 minutes. This could be broken up into smaller segments if required. You should aim
to do at least 20 trials each day. If the child masters this stage in one session, introduce
the next stage in the same day. Try to get through the training stages as quickly as
possible. This may mean that you master a few stages in one day
Teaching Procedure
1. Determine reinforcement
Ask the child what they would like to exchange their tokens for at the end of the session
(in keeping with how you usually do in your session). Use stimulus preference
assessments if necessary.
2. Set the device
Set the vibrating devise to buzz at 30 second intervals (FI schedule). This should give
enough time to prompt and provide quick reinforcement. If not, discuss with Corinna,
Pagona or Maria to adjust the time settings.
3. Child reads rule card
SD1: “Today you will be practicing with me how you can ask your friends questions”
(Hand child a rule card). “Let’s read what it says on this card”
I can get tokens for asking my friends questions. I can say:
Where do you live?
When’s your birthday?
Can I play with you?
Do you have any pets?
What’s
favourite
programme?
R1: Child should
read your
the card,
but TV
help
with any words that he finds difficult.
4. Child asks questions when cued by the buzzer
Appendices
Immediately after the child has read the questions on the rule card use least-to-most
prompting procedures to teach the child how to ask the questions when cued by the
buzzer.
Step one: Unprompted trials
Because of the high levels of prompting in previous phases of teaching. You will start
this training phase with no prompts, but then use prompts if needed following the least to
most prompting procedure (see prompting suggestions below).
SD1: “Lets practice now using the buzzer and asking these questions”. (Put the buzzer
in the child pocket and place the child’s hands on top of the table “Each time you ask me
a question from the card I will give you a token”
If it is easier, or more preferred for the child to have their hands in a different position
(e.g., in their lap but still not touching the motivaider) then consult with Corinna, Pagona
or Maria. This would be OK, but the important thing is the consistency, everyone should
be teaching the same position with the hands.
So that you know when the buzzer has vibrated in the child’s pocket start a timer at the
same time as the buzzer. Every 30 seconds you would know to prompt the child if no
question was forthcoming.
R1: When the buzzer vibrates, child asks question on the card
C: Nice asking (and give a token), and then provide a quick response to each child’s
question (Thus, if they say, “Can I play with you?” say “yes, Lets play the tickling game”
and give them a quick tickle- choose an activity that means that the child can stay sitting
down at the table).
If they have asked a social question (e.g., when’s your birthday?”), sometimes answer
and then repeat the question (i.e., reciprocal social questions), however you are not
taking data on this and they do not have to respond (although it would be nice if they
did!).
Every five trials present a different rule card that has the questions written on in a
different order. Thus, if the child immediately asks all questions correctly and masters
the stage then there is no need for a new rule card. However, if they make some errors
and need more than five trials to master a stage then you would need to rotate the cards
so they see the questions in a different order every five trials.
Data Collection:
On the trial by trial data sheet:
Correct Response: When their hand is not in direct contact with the motivaider, child
says a different question on the rule card on consecutive trials clearly so that it can be
understood. Says a socially appropriate question that is not on the rule card.
Incorrect Response: Child has hand on the motivaider when they are buzzed; No
response within 3 seconds of vibration; Gives an inappropriate statement or question
(e.g., verbal stereotypy; swearing); speaks unclearly so that the question cannot be
understood; saying the same question on consecutive trials (if they say the same
question two or three trials later this is acceptable). Indicate the error made in the margin
171
Appendices
(NR- no response; IQ- Inappropriate question; US- Unclear speech; Rpt- Repeated
question)
On the skills tracking sheet: Record the date each target was introduced and mastered.
Prompting Suggestions:
(1) Use least to most prompts, as described in Stage two (e.g., if ‘jiggling’ the card
to bring their attention to it doesn’t work, then point to a question on the card, if
this also doesn’t work then also use a verbal cue “You need to ask me a
question”, at the same time as pointing.
(2) For inappropriate questions- therapist should model an appropriate question
(3) For unclear speech- therapist should say, “Say it clearly” and present an echoic
trial (e.g., “Say, What’s your name?”).
(4) For saying the same question on consecutive trials- therapist, should say, “You
need to ask a different question (and point to a different question on the rule
card)”
Mastery Criterion: Using trial by trial data, five consecutive correct trials with no
prompts
172
Appendices
173
Teaching Plan Eye contact when asking
questions
Stage Five
Medium Term Objective: With rule card on the table in front of they child, they will look
at you each time they ask the question. The motivaider will be in their pocket and the
child’s hand will not be on top.
Materials: Motivaider, child’s file, data sheets, rule cards, tokens and token board,
reinforcers
Frequency of training: Conduct two training sessions a day, each lasting approximately
10 minutes. This could be broken up into smaller segments if required. You should aim
to do at least 20 trials each day. If the child masters this stage in one session, introduce
the next stage in the same day. Try to get through the training stages as quickly as
possible. This may mean that you master a few stages in one day
Teaching Procedure
1. Determine reinforcement
Ask the child what they would like to exchange their tokens for at the end of the session
(in keeping with how you usually do in your session). Use stimulus preference
assessments if necessary.
2. Set the device
Set the vibrating devise to buzz at 30 second intervals (FI schedule). This should give
enough time to prompt and provide quick reinforcement. If not, discuss with Corinna,
Pagona or Maria to adjust the time settings.
3. Child reads rule card
SD1: “Today you will be practicing with me how you can ask your friends questions”
(Hand child a rule card). “Let’s read what it says on this card”
I can get tokens for asking my friends questions. I can say:
Where do you live?
When’s your birthday?
Can I play with you?
Do you have any pets?
What’s
favourite
programme?
R1: Child should
read your
the card,
but TV
help
with any words that he finds difficult.
Appendices
4. Child asks questions with eye contact
Immediately after the child has read the questions on the rule card use most-to-least
prompting procedures to teach the child how to ask the questions with eye contact when
cued by the buzzer.
Step one: Prompted trials
SD1: “Lets practice now you looking at me when you ask me the questions”
(Put the buzzer in their pocket, their hands should not be on top of the buzzer). “Each
time you ask me a question and look at me, I will give you a token”
SD2: When the buzzer vibrates, tap the bridge of your nose at the same time as saying
“Look at me”.
So that you know when the buzzer has vibrated in the child’s pocket start a timer at the
same time as the buzzer. Every 30 seconds you would know to prompt the child if no
question was forthcoming.
R: Child asks question on the card with eye contact
C: Lovely looking (and give a token), and then provide a quick response to each child’s
question (Thus, if they say, “Can I play with you?” say “yes, Lets play the tickling game”
and give them a quick tickle. Always choose an activity that means that the child can
stay sitting down at the table).
If they have asked a social question (e.g., when’s your birthday?”), sometimes answer
and then repeat the question (i.e., reciprocal social questions), however you are not
taking data on this and they do not have to respond (although it would be nice if they
did!).
Every five trials present a different rule card that has the questions written on in a
different order. Thus, if the child immediately asks all questions correctly and masters
the stage then there is no need for a new rule card. However, if they make some errors
and need more than five trials to master a stage then you would need to rotate the cards
so they see the questions in a different order every five trials.
Step two: Unprompted trials
Keep rule card on the table in front of the child. Fade the following prompts:
(1) Change instructional SD from “Lets practice now you looking at me when you ask
me the questions” to the SD used in previous stages “Lets practice now using the
buzzer and asking these questions”
(2) When the motivaider vibrates fade saying “you need to look at me” then tapping
your nose.
Continue, as above until child asks a different question with eye contact unprompted for
five consecutive trials.
Prompting Suggestions:
For eye contact
174
Appendices
(1) If the child is not looking at you when they ask the question, say, “You need to
look at me, when you ask me the question”. If this doesn’t bring about the desired
response then lightly tap the bridge of your nose at the same time as saying “you
need to look at me”. Fade as soon as possible.
(2) Change the SD above, so you include a cue for looking, (e.g., “Lets practice now
using the buzzer and you looking at me when you ask me these questions”
(3) If eye contact continues to be a problem they could be given new rule cards
which say “I can get tokens for looking at my friends when I ask questions”
For asking questions
(4) Use least to most prompts, as described in previous stages for the child to ask
the questions from the rule card (e.g., if ‘jiggling’ the card to bring their attention
to it doesn’t work, then point to a question on the card, if this also doesn’t work
then also use a verbal cue “You need to ask me a question”, at the same time as
pointing.
(5) For inappropriate questions- therapist should model an appropriate question
(6) For unclear speech- therapist should say, “Say it clearly” and present an echoic
trial (e.g., “Say, What’s your name?”).
(7) For saying the same question on consecutive trials- therapist, should say, “You
need to ask a different question (and point to a different question on the rule
card)”
Data Collection:
On the trial by trial data sheet:
Correct Response: Says a different question on the rule card on consecutive trials
clearly so that it can be understood and looks at you when they ask the question. Says
a socially appropriate question that is not on the rule card with eye contact.
Incorrect Response: Does not look at you when they ask the question, no response
within 3 seconds of vibration; Gives an inappropriate statement or question (e.g., verbal
stereotypy; swearing); speaks unclearly so that the question cannot be understood;
saying the same question on consecutive trials (if they say the same question two or
three trials later this is acceptable). Indicate the error made in the margin (NL- no
looking; NR- no response; IQ- Inappropriate question; US- Unclear speech; RptRepeated question)
On the skills tracking sheet: Record the date each target was introduced and mastered.
Mastery Criterion: Using trial by trial data, five consecutive correct trials with no
prompts
175
Appendices
176
Teaching Plan Repeating question after non
response (“persistence”)
Stage Six
Medium Term Objective: With rule card on the table in front of they child, they will still
look at you each time they ask the question. The motivaider will be in their pocket and
the child’s hand will not be on top. In addition, the child will repeat the question once if
you do not answer the question the first time
Materials: Motivaider, child’s file, data sheets, rule cards, tokens and token board,
reinforcers
Frequency of training: Conduct two training sessions a day, each lasting approximately
10 minutes. This could be broken up into smaller segments if required. You should aim
to do at least 20 trials each day. If the child masters this stage in one session, introduce
the next stage in the same day. Try to get through the training stages as quickly as
possible. This may mean that you master a few stages in one day
Teaching Procedure
1. Determine reinforcement
Ask the child what they would like to exchange their tokens for at the end of the session
(in keeping with how you usually do in your session). Use stimulus preference
assessments if necessary.
2. Set the device
Set the vibrating devise to buzz at 45 second intervals (FI schedule). The time interval is
increased to allow extra time for a non response and for the question to be repeated.
This should give enough time to prompt and provide quick reinforcement. If not, discuss
with Corinna, Pagona or Maria to adjust the time settings.
3. Child reads rule card
SD1: “Today you will be practicing with me how you can ask your friends questions”
(Hand child a rule card). “Let’s read what it says on this card”
I can get tokens for asking my friends questions. I can say:
Where do you live?
When’s your birthday?
Can I play with you?
Do you have any pets?
What’s
favourite
programme?
R1: Child should
read your
the card,
but TV
help
with any words that he finds difficult.
Appendices
4. Child asks questions with eye contact
Immediately after the child has read the questions on the rule card use most-to-least
prompting procedures to teach the child how to repeat the question when you do not
answer
Step one: Prompted trials- non response every trial
SD1: “Lets practice now you repeating the question when I do not answer”
(Put the buzzer in their pocket, their hands should not be on top of the buzzer). “Each
time you ask me a question again, I will give you another token”
So that you know when the buzzer has vibrated in the child’s pocket start a timer at the
same time as the buzzer. Every 30 seconds you would know to prompt the child if no
question was forthcoming.
R1: The child asks you a question when the motivaider buzzes
C/SD2: You still provide a token for the first question but do not respond
Prompt: Wait three seconds, and then say “I didn’t answer. You need to ask me the
question again” at the same time as pointing to the same question they asked previously
R2: Child asks the question on the card a second time with eye contact
C2: Lovely asking me again (and give a token)
Step two: Unprompted trials- non response every trial
Keep rule card on the table in front of the child
Fade ‘you need to ask me the question again” prompts first, followed by pointing
prompts, and only provide tokens for unprompted trials.
Continue, as above until child can repeat the question for five consecutive trials when
you do not respond first time.
Step three: Intermix trials so that sometimes you respond immediately sometimes you
don’t
With no prompts child can differentiate between when they need to repeat the same
question after you have not answered their question and when they can move onto a
different question on the next trial when you answer first time.
Continue, as above until child can answer correctly for ten consecutive trials (i.e., five
each of them having to repeat the question versus when they don’t have to repeat the
question).
Data Collection:
On the trial by trial data sheet:
Correct Response:
For non responses: After your non response to their question they repeat the same
177
Appendices
question again (with eye contact) within 5 seconds of when they initially asked the
question.
Other trials: Says a different question on the rule card on consecutive trials clearly so
that it can be understood and looks at you when they ask the question. Says a socially
appropriate question that is not on the rule card with eye contact.
Incorrect Response:
For non responses: The child does not repeat any question within 5 seconds of the non
response; child asks a different question within the five seconds (i.e., they don’t repeat
the previous question). Indicate in the margin NP (No persistence) for this error
Other trials: Does not repeat any question after non response; Repeats a different
question after the non response; Does not look at you when they ask the question, no
response within 3 seconds of vibration; Gives an inappropriate statement or question
(e.g., verbal stereotypy; swearing); speaks unclearly so that the question cannot be
understood; saying the same question on consecutive trials (if they say the same
question two or three trials later this is acceptable). Indicate the error made in the margin
(NL- no looking; NR- no response; IQ- Inappropriate question; US- Unclear speech; RptRepeated question;
On the skills tracking sheet: Record the date each target was introduced and mastered.
Prompting Suggestions:
For repeating questions
(1) Use prompts, as described above, when you first introduce this program
(2) It may be useful to have a second person to prompt
(3) It may also be useful to write on the rule card the additional requirement. For
example, “I can get tokens for looking at my friends when I ask questions and for
remembering to ask again when they don’t answer”
(4) If they ask a different question, remind them that it needs to be the same
question and point to it on the rule card.
For other trials
(1) See previous stages
Mastery Criterion:
Step two: Using trial by trial data, five consecutive correct trials with no prompts
Step three: ten consecutive correct trials (5 each of when you respond first time versus
when you don’t respond first time)
178
Appendices
179
Teaching Plan Generalizing setting
Stage Seven
Medium Term Objective: With child in the setting that they will be for the intervention
phase (e.g., main school play ground, main hall) child will be able demonstrate all of the
previously acquired skills (e.g., asking questions with eye contact, repeating questions)
in response to the buzzer. In addition, they will hold the rule card to remind themselves
of the questions and will be able to approach the therapist from across the
room/playground to make the initiation.
Materials: Motivaider, child’s file, data sheets, rule cards, tokens and token board,
reinforcers
Frequency of training: Conduct two training sessions a day, each lasting approximately
10 minutes. This could be broken up into smaller segments if required. You should aim
to do at least 20 trials each day. If the child masters this stage in one session, introduce
the next stage in the same day. Try to get through the training stages as quickly as
possible. This may mean that you master a few stages in one day
Teaching Procedure
1. Determine reinforcement
Ask the child what they would like to exchange their tokens for at the end of the session
(in keeping with how you usually do in your session). Use stimulus preference
assessments if necessary.
2. Set the device
Set the vibrating devise to buzz at 1 min intervals (FI schedule). The schedule has been
changed to a fixed interval 1 min schedule to allow time for prompting but also so that it
is more in keeping with the next phase of this study.
3. Child reads rule card
SD1: “Today you will be practicing with me how you can ask your friends questions”
(Hand child a rule card). “Let’s read what it says on this card”
I can get tokens for asking my friends questions. I can say:
Where do you live?
When’s your birthday?
Can I play with you?
Do you have any pets?
What’s your favourite TV programme?
Appendices
R1: Child should read the card, but help with any words that he finds difficult.
SD2: Now let’s put the card in your pocket. If you forget what to say, you can take the
card out of your pocket and read one of the questions
R2: Child puts card in their pocket
4. Child approaches you to ask questions
Immediately after the child has put the card in their pocket. Set the motivaider to a FI 1
minute schedule and put in the child’s pocket. Set your timer/ motivaider so you know
when to prompt. They should be encouraged to go and play with something in the room,
run around the hall (i.e., you should not be next to them and preferably they should be
engaged in an activity when the motivaider vibrates even if it is just walking around).
Step one: Prompted trials- therapist standing in the same position
SD1: “Lets practice now using the buzzer and you coming and asking me these
questions when I stand here. You can go and play over there (and point to the other side
of the room/ playground. Each time you walk up to me and ask me a question from the
card I will give you a token”.
R1: Child goes to where they have been instructed to play/ stand. Therapist stays where
they are.
SD2 (prompted trial): When the buzzer vibrates, say “Come over here and ask me a
question” (if necessary, provide further prompts for the child to stand immediately in front
of you and to provide eye contact when they ask the question)
R2: Child approaches you and asks question
C: Nice asking (and give a token), and then provide a quick response to each child’s
question (Thus, if they say, “Can I play with you?” say “yes, Lets play the tickling game”
and give them a quick tickle. Always choose an activity that means that the child can
stay sitting down at the table).
Other prompting Suggestions:
(1) If the child approaches you but does not ask a question prompt the child to take
the rule card out of their pocket and to choose a question from the card.
Gradually fade these prompts over successive trials.
(2) If the child approaches you but has incorrect body orientation (e.g., does not face
towards you, stands too far away, etc) target this separately. You could, for
example, provide a visual marker (e.g., a chalk line) to show the child where they
need to stand but this should be gradually faded.
(3) For other errors- see previous stages for prompting suggestions
Step two: Unprompted trials- therapist standing in the same position
Fade ‘Come over here and ask me a question’ prompts first and then other prompts,
until you are only providing tokens for unprompted trials.
Continue, as above until child asks a different question unprompted for five consecutive
trials when you stand in the same position in the hall/ play ground
180
Appendices
Step three: Unprompted trials- therapist standing in different positions in the hall/
playground
Move to a different position for each trial, so that the child has to scan the room/
playground to find you. Continue, as above until child asks a different question
unprompted for five consecutive trials when you stand in different positions in the hall/
play ground
Step four: Generalize persistence (i.e., intermix trials so that sometimes you respond
immediately sometimes you don’t)
Same as step three, except occasionally do not respond to the child’s question.
Continue, until child can answer correctly for five consecutive trials (i.e., three each of
them having to repeat the question versus two trials when they don’t have to repeat the
question).
Data Collection:
On the trial by trial data sheet:
Step two and three
Correct response: Child walks across the room/ playground and asks you a question
with eye contact when they are standing immediately in front of you. They should not
need to look at their rule card for a reminder.
Incorrect response: Child does not approach you to ask question, child asks question but
is standing too far away or does not have eye contact. Child needs to use rule card to
ask you a question.
Other incorrect responses (as previous stages): Does not look at you when they ask the
question, no response within 3 seconds of vibration; Gives an inappropriate statement or
question (e.g., verbal stereotypy; swearing); speaks unclearly so that the question
cannot be understood; saying the same question on consecutive trials (if they say the
same question two or three trials later this is acceptable).
Step four: Persistence
Correct responses- After therapists’ non response: After your non response to their
question they repeat the same question again (with eye contact) within 5 seconds of
when they initially asked the question.
Incorrect responses- For non responses: The child does not repeat any question within 5
seconds of the non response; child asks a different question within the five seconds (i.e.,
they don’t repeat the previous question).
Other incorrect responses (as previous stages): Does not look at you when they ask the
question, no response within 3 seconds of vibration; Gives an inappropriate statement or
question (e.g., verbal stereotypy; swearing); speaks unclearly so that the question
cannot be understood; saying the same question on consecutive trials (if they say the
same question two or three trials later this is acceptable).
On the skills tracking sheet: Record the date each target was introduced and mastered.
Mastery Criterion:
Step two: Using trial by trial data, five consecutive correct trials with no prompts
Step three: Using trial by trial data, five consecutive correct trials with no prompts
Step four: Using trial by trial data, five consecutive correct trials with no prompts (i.e., 3
181
Appendices
trials repeating question after a non response 2 trials where they do not need to repeat
the question).
182
Appendices
183
Teaching Plan Generalizing person and delaying
Stage Eight token delivery
Medium Term Objective: With child in the setting that they will be for the intervention
phase (e.g., main school play ground, main hall) child will be able demonstrate all of the
previously acquired skills (e.g., approaching adult from across the room to ask question
in response to the buzzer) but with an adult who has not been involved with the previous
stages of training. In addition, their therapist will ‘brief’ them before hand about what they
are expected to do and ‘debrief them’ afterwards, including giving them the tokens they
have amassed during the training session.
Materials: Motivaider, child’s file, data sheets, rule cards, tokens and token board,
reinforcers
Frequency of training: Conduct two training sessions a day, each lasting approximately
10 minutes. This could be broken up into smaller segments if required. You should aim
to do at least 20 trials each day. If the child masters this stage in one session, introduce
the next stage in the same day. Try to get through the training stages as quickly as
possible. This may mean that you master a few stages in one day
Teaching Procedure
1. Determine reinforcement
Ask the child what they would like to exchange their tokens for at the end of the session
(in keeping with how you usually do in your session). Use stimulus preference
assessments if necessary.
2. Set the device
Set the vibrating devise to buzz at 1 min intervals (FI schedule). The schedule has been
changed to a fixed interval 1 min schedule to allow time for prompting but also so that it
is more in keeping with the next phase of this study.
3. “Briefing” child before session
Briefing Statement
“Today you will be asking (name of person who does not usually work with child) these
questions (and go through questions with child)
“I can get tokens for asking my friends questions”. I can say:
Where do you live?
When’s your birthday?
Can I play with you?
Do you have any pets?
What’s your favourite TV programme?
Appendices
I am going to hold onto the card for you, and stand over here and see how well you do
remembering to ask XX the questions. Each time I see you ask (XXX) a question and I
see you looking and standing close to XXX, I am going to put a token on your board.
You will not see me give you a token each time, but at the end, I’ll call you over and we
can see how well you have done. OK let’s start (put the motivaider in child’s pocket set
to a FI 1 min schedule). Go and play over there and remember to ask XXX the questions
when you feel the buzzer (and child goes to the specified location).
4. Child approaches adult (not involved in training) to ask the questions.
Step one: Unprompted trials- unfamiliar adult in varied locations in the hall/ playground
Because of the high levels of prompting in the previous phases of teaching. You will start
this training phase with no prompts, but then use prompts if needed following the least to
most prompting procedure (see below).
SD1: Child is playing/ walking around the room/ playground. Unfamiliar adult is in the
same location a few feet away. Therapist is at the side of the room/ playground holding
the token board. They have a timer/ motivaider so that they know when the child’s
devise has gone off to prompt if necessary. Child’s motivaider goes off.
R1: Child approaches adult and asks the question
C: Therapist notes the correct response on the data sheet, and puts a token on the
token board
Prompting suggestions
All prompts should be delivered by the therapist and not the unfamiliar adult.
(1) If the child does not approach the unfamiliar adult within 5 second of the
vibration, the therapist could say from across the room, “remember you need to
ask XX questions when you feel the buzz in your pocket”
(2) If the child approaches the adult but does not ask a question, the therapist could
quickly show them the question prompt card.
(3) If the child approaches the adult but has incorrect body orientation (e.g., does not
face them, stands too far away, etc) target this separately. You could, for
example, provide a visual marker (e.g., a chalk line) to show the chills where they
need to stand but this should be gradually faded.
(4) For other errors- see previous stages for prompting suggestions
Debriefing statement
After the session (approximately ten minutes) call the child over to debrief them.
“Lets see how well you did. You got (five tokens) for asking XXX questions. Well done!”
Point out what went well during the session- (For example) “You really remembered the
questions very well, and stood right in front of her when you asked the questions”
Point out what did not go so well during the session- (For example) “Sometimes, you
forgot to look at her when you asked the question, so I could not give you tokens for
184
Appendices
those questions. Try to remember to do that next time”.
Data Collection:
On the trial by trial data sheet:
Correct response: Child walks across the room/ playground and asks the unfamiliar adult
a question with eye contact when they are standing immediately in front of them. They
should not need to look at their rule card for a reminder.
Incorrect response: Child does not approach adult to ask question, child asks question
but is standing too far away or does not have eye contact. Child needs to use rule card
to ask the question.
On the skills tracking sheet: Record the date each target was introduced and mastered.
Mastery Criterion:
Five consecutive correct trials with no prompts
185
Appendices
186
Appendix 3
Samples of rule cards
3a. Rule card used with Alex and Peter
3b. Rule card used with Reuben
3c. Rule card used with Katie
Appendices
187
Appendix 3a
Rule card used with Alex and Peter
I can get tokens for asking my friends questions. I can say:
Do you have any pets?
Where do you live?
Can I play with you?
What’s your favourite TV programme?
When is your birthday?
A buzzer will remind me when to ask a question to a friend.
Appendices
188
Appendix 3b
Rule card used with Reuben
I can talk to my friends. When I feel my
buzzer I can say:
“Hello!” and get a token, or...
“Can we play?” and get a token.
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189
Appendix 3c
Rule card used with Katie
My rule card:
I can get tokens for asking my friends questions. I can
say:
Can I play too?
Do you have a Wii?
Do you wa t to da ce like Britai ’s Got Tale t?
Do you watch Horrid Henry?
What’s your a e?
A buzzer will remind me when to speak to my friend.
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190
Appendix 4
Information to participants (Chapter 4)
4a. Information sheet for parents
4b. Consent form
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191
Appendix 4a
Information Sheet for Parents (Form A)4
Study title
An evaluation of the use of the Maths Recovery Program to teach numeracy to children with
autism
Project team
Pagona Tzanakaki, Research student
Corinna Grindle, PhD, BCBA, Consultant Behaviour Analyst
Richard Hastings, Professor of Psychology
Carl Hughes, PhD, BCBA, Course Director of ABA MSc
This research project is being carried out by Bangor University.
Purpose of the study
Children with autism – as you are probably aware – often need to be taught in a very
structured and systematic way in order to learn. For this reason detailed teaching procedures
are being used in ABA programs to teach a variety of skills, e.g. language, play, self-help
skills etc. However, in the area of mathematics, a detailed curriculum has not yet been
developed. The existing ABA teaching manuals include only a few numeracy targets. We
believe that a more systematic numeracy program will be helpful for children with autism in
ABA programs and the teaching staff who work with them.
4
We had planned to use Form B with participants of a control group that would be recruited from other ABA
schools, however this did not prove possible; therefore only Form A was used.
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192
The Maths Recovery Program is a detailed curriculum that has been designed to help teach
numeracy to young children. It was originally developed in Australia for typically developing
children who face difficulties in mathematics and is now being used in many countries
around the world, including some schools in the UK. Because Maths Recovery has many
characteristics in common with the teaching methods used in ABA programs (e.g. breaking a
task into small steps, one to one teaching, etc) we believe that it can be effectively used as the
basis of a numeracy curriculum for children with autism.
A number of studies which have already been conducted to evaluate Maths Recovery have
shown that it is an effective numeracy program. All these studies have involved typically
developing children. Since no research has yet been done with children with autism, we are
interested in investigating how these children progress when taught with the program and
compare their progress with that of children who are taught with the usual teaching manuals.
Procedures involved
We intend to use two groups of KS-1 and KS-2 children for the purposes of the study. Group
A (Westwood School) children will be taught with the Maths Recovery program. (Maths
Recovery is already being used in Westwood, both in the mainstream and in the ABA unit
but no systematic evaluation has been done yet). Group B (children enrolled in other ABA
schools) will continue to be taught with the maths curriculum currently in use by their school.
Personnel in the schools have expressed interest in participating in the study, in the condition
that the investigators will provide training to staff members on the use of Maths Recovery.
The following procedure will be used:
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193
1. At the beginning of the study children in both groups will complete a few
standardized numeracy tests.
2. For the rest of the school year the children of group A will receive systematic
numeracy instruction based on Maths Recovery. This will be delivered by the tutors
who normally work with each child and will take place during the ordinary school day
for approximately 30 minutes (per day).
3. At the end of the school year children in both groups will again be tested using the
same standardized tests used in the beginning of the study.
4. To ensure that all tutors implement the teaching procedures correctly, it is possible
that some of the teaching sessions might be videotaped. The video tapes will only be
viewed by the research team members and will be kept in a secure cabinet until data
analysis has been completed. They will be destroyed after that.
We would like to request your child’s participation in group A.
What are the benefits of taking part?
The main benefits of this research relate to improving the knowledge that we have on the best
teaching practices for children with autism. Numeracy and mathematical skills in general
have been shown to be an important component of success in school and are necessary in
almost any vocational environment. But, more importantly, math skills are essential in
everyday life activities such as cooking and managing personal finances. Consequently, in
any population, including persons with autism, independence is partly determined by
competency in math skills. We hope that the results of this study will help professionals
working in school- and home-based programmes for children with autism by providing them
Appendices
194
with a detailed curriculum that can be used with children across a wide range of numeracy
skills.
Are there any risks involved?
We do not believe that the children participating in the study are being put in risk in any way.
Your child’s identity will be protected at all times and the completed study will not include
their name, the name of the school, or any other identifying information.
Your participation is completely voluntary and you reserve the right to withdraw your child
from the study at any time without giving any explanations and without this affecting his/her
education in any way. If you have any further queries about the study please do not hesitate to
contact us, our details are below.
Pagona Tzanakaki
Postgraduate Research Student
The ABA Class
Westwood Primary School
Tabernacle Street
Buckley, Flintshire
CH7 2JT
Email: [email protected]
Tel: 01244 545731
Or
Dr Corinna Grindle
Consultant Behaviour Analyst
The ABA Class
Westwood Primary School
Tabernacle Street
Appendices
Buckley, Flintshire
CH 7 2JT
Email: [email protected]
Tel: 01244 545731
If you have any complaints about how this study is conducted please address these to:
Professor Oliver Turnbull
Head of School of Psychology
Bangor University
Gwynedd
LL57 2DG
195
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196
Appendix 4b
Research Consent Form for Parents
Please complete the following and circle as necessary:
6. Have you read the information on the Information sheet?
YES / NO
Have you had an opportunity to ask questions and discuss this study?
YES / NO
Have you received satisfactory answers to all your questions?
YES / NO
7. Do you give consent for your child to participate in the study?
YES / NO
8. Do you give consent for your child to be videoed?
YES / NO
9. Are you aware that once research has been completed these video tapes will be
destroyed?
YES / NO
10. Are you aware that you can withdraw your child from the study at any time without
giving a reason for withdrawing?
11. Would you like a copy of this consent form?
YES / NO
YES / NO
12. Would you like to be sent a copy of the study or, if it is published, a copy of the
printed article?
YES / NO
Signature______________________________________________________________
Date__________________________________________________________________
Your name ____________________________________________________________
Your child’s name ______________________________________________________
Address_______________________________________________________________
______________________________________________________________________
____________________________Postcode__________________________________
Please return this form, at your earlier convenience, to Pagona Tzanakaki at the ABA Class in Westwood
School.
Appendices
197
Appendix 5
Letter sent to parents to ask for permission for a follow-up test
5a. Information letter
5b. Consent form
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198
Appendix 5a
Information letter
Dear parents
During the previous school year (2009-10) we conducted a study on the use of a Mathematics
curriculum called Maths Recovery with young children with autism. Maths Recovery had
been shown to help typically developing children who have difficulties in maths and our
purpose was to investigate whether it could be effective with children with autism as well.
To be able to measure the progress of the children we tested them with some standardized
numeracy tests at the beginning and the end of the teaching period. As you probably
remember, we asked your permission at the beginning of the school year to conduct the tests
with your child (see the Information Sheet attached to this letter).
The results we have so far are encouraging and suggest that Maths Recovery helps children
with autism make good progress in their numeracy skills. However, especially as there have
been no previous studies on Maths Recovery and children with autism, we would like to see
if the improvements we saw have been maintained after the summer holiday. So we are
asking for your permission to repeat one of the tests that your child has previously done.
Depending on the child’s ability level, testing time will be between 15 and 60 minutes. It can
take place either at school or at home.
Thank you
Pagona Tzanakaki
Research student
Tel.: 07901992001
E-mail: [email protected]
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199
Appendix 5b
Consent Form
Please complete the following and circle as necessary:
1. Do you give consent for your child to be tested?
2. Where would you prefer the testing to take place?
YES/NO
School / Home
Signature______________________________________________________________
Date__________________________________________________________________
Your name ____________________________________________________________
Your child’s name ______________________________________________________
Address_______________________________________________________________
______________________________________________________________________
____________________________Postcode__________________________________
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200
Appendix 6
Sample lesson from the adapted Maths Recovery curriculum for children with ASD
Teaching Plan
A2.3
Emergent-Sequencing Numerals
Key Topic: Numerals from 1 to 10
Medium Term Objective: Child will be able to put in order (i.e., sequence) numbers 1 to 10
Materials: Number cards 1-10. Black numbers on white card. All numbers to be the same
proportion. Numbers to be written as follows: 1 2 3 4 5 6 7 8 9 10
Teaching Procedure:
Step one: For numbers 1-3: Arrange 3 number cards on the table in disarray (i.e., in no
particular order or position), establish attending and say to the child “Put in order”. Prompt the
child to place the cards on the table in the correct order, from left to right, and reinforce the
response. Fade prompts over subsequent trials. Differentially reinforce responses demonstrated
with the lowest level of prompting. Eventually, only reinforce correct unprompted responses.
Step two: After the task has been mastered with numbers 1-3 move on to numbers 1 to 4, 1 to 5,
4 to 7, 6 to 9, 6 to 10, 1 to 6, 1 to 8, 1 to 10. Remember to probe the later sequences immediately
before introducing a new one. If the child probes correct on first trial then you may not need to
formally teach that sequence.
Step three - generalization: When the child has become fluent at using the skill, therapists
should start to set up opportunities for generalization training (i.e., when different materials are
presented, by different people, in different settings).


For generalization across stimuli the child could be taught to sequence numbers with
different number cards (i.e., different fonts, different colours, different sizes, number
cards from a game etc). You could also check to see if the child can put cards in order
from top to bottom instead of left to right although this is not necessary for mastery of the
skill.
For generalization across SDs, instructions could include “Put these in the correct order
“Sequence these numbers”).
Appendices
 Present the task in a different setting
 Have a different person present the task
Prompting Suggestions:
(1) Initially a blank grid could be used so that the children have somewhere to place their
numbers.
(2) Use positional prompts: Placing the number cards near or adjacent to where they should
go (i.e., the numbers are not initially presented in disarray).
(3) Use backward chaining teaching procedures (e.g., for 1-2-3):
Step one: Therapist puts cards 1-2 out in correct order and child is required to bring down
number 3 and place next to the 2.
SD: Put in order (therapist points to 1 + 2 saying each number at the same time as she points
to it)
R: Child brings down number 3 and places it next to the 2.
C: Therapist labels 3 as child brings it down and delivers praise
Thus, although child is not required to label the numbers as he/ she sequences them, the
therapist should still label them.
Step two: Therapist puts card # 1 on the table and child is required to bring down numbers 2
and 3 and position correctly.
All prompts should be faded for mastery of the skill.
Mastery Criterion: 3 consecutive yes probes (across sessions) on first trial data. Under the
direction of the consultant this can be changed to 3 consecutive yes probes across days, across
days with a 3 day retention period, or to trial-by-trial data (e.g., 10 consecutive correct
responses). However, before introducing each new number sequence the remaining sequences to
be taught must first be probed to see if the child probes correct without being formally taught. It
is quite possible that they will acquire the concept before you formally teach all the number
sequences.
Fluency: Teaching to fluency will not be required for this skill.
Data Collection:
On the probe data sheet: Always take probe data on the first trial of the session for all current
targets. The child should not be prompted for these responses.
Correct Response: Puts numbers in the correct position within 3 seconds of the SD when all
numbers have been placed in a random position on the table and there is no grid being used for
the child. Once the child has placed the first number card, additional numbers should be placed
within one second of each other. The child is not required to say the number as they bring it down
for mastery of the skill.
Incorrect Response: Puts numbers in incorrect order, does not respond within 3 sec of the SD,
201
Appendices
places numbers slower than one number every second.
Switch to trial by trial data collection if advised by your consultant
On the skills tracking sheet: Record the date each target was introduced and mastered.
202
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203
Appendix 7
Information to participants (Chapter 5)
7a. Information sheet for parents
7b. Consent form
Appendices
204
Appendix 7a
Information Sheet for Parents
Study title
An evaluation of the use of the Maths Recovery Program to teach numeracy to lowperforming KS-1 and KS-2 students with learning disabilities
Project team
Pagona Tzanakaki, Research student
Carl Hughes, PhD, BCBA, Course Director of ABA MSc
Richard Hastings, Professor of Psychology
Corinna Grindle, PhD, BCBA, Consultant Behaviour Analyst
This research project is being carried out by Bangor University.
Purpose of the study
Many children with learning disabilities have difficulty learning maths skills at school even
though they receive maths teaching in school. We are carrying out a research project to test
whether if children with a learning disability are taught in a more intensive and individualized
way, their maths skills can improve.
The Maths Recovery Program is a detailed curriculum that has been designed to help teach
numeracy skills to young children. It was originally developed in Australia for typically
developing children who face difficulties in mathematics and is now being used in many
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205
countries around the world, including some schools in the UK. With this teaching program
the child is being taught individually, usually for 30 minutes per day.
We believe that although Maths Recovery was developed with typically developing children
in mind, it can also be an appropriate curriculum for children who have a learning disability.
One important aspect of the program is that because each child is taught individually, the
pace of teaching can be adjusted to the child’s abilities and rhythm of learning. So, if the
child has difficulty with a task, the teacher can break it into smaller, easier steps, model the
appropriate maths skills, spend more time with particular tasks, etc. We have already used the
program –with some adaptations – to teach a group of Key Stage 1 children with autism who
also had learning disabilities and the results were very encouraging. We now hope to show
that children with learning disabilities can also benefit from the Maths Recovery model.
Procedures involved
Your child’s class teacher has suggested that (s)he might benefit from some additional
structured teaching on maths skills.. We will provide training on Maths Recovery to teaching
assistants who work in your child’s class so that they can teach the children. Because every
child will be taught individually and we can only train a limited number of teaching
assistants, we will not be able to offer the Maths Recovery teaching to every child at Ysgol y
Gogarth in the current school year. Only one half of the children identified by class teachers
will be taught with Maths Recovery this school year, while (if Maths Recovery works well)
the other half will start on this teaching in the new school year in September 2011.
Children who do not receive the Maths Recovery teaching in January to July 2011 will
continue to receive maths teaching as they normally do in their class.
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206
Once you have given consent for your child to take part in this project, we intend to use the
following procedure:
5. At the beginning of the research study, all children will complete a few standardized
maths tests.
6. The children will be randomly divided (using a computer programme – like tossing a
coin to decide) in two groups:
Those randomly allocated to the first group will receive numeracy teaching based on
Maths Recovery for about six months (January to July). This will be delivered by
teaching assistants who work in your child’s school and will take place during the
ordinary school day for approximately 30 minutes per day. Pagona Tzanakaki, who is
a qualified teacher and jointly developed the maths recovery model for children with
autism, will be supervising the training of the teaching assistants. It is possible that
Pagona might be involved with teaching your child maths skills as well.
During January to July, children randomly allocated to the second group will receive
maths teaching in the same format they were previously taught by the school.
7. At the end of the school year in July, children in both groups will again be tested
using the same standardized maths tests used in the beginning of the study.
8. If the tests show that the children of the first group have made more progress at the
end of the school year than those from the second group, the second group will start
the Maths Recovery teaching after the summer holidays in September 2011.
Since children will be randomly allocated into the two groups, your child might either be
in the first or in the second group
Appendices
207
What are the benefits of taking part?
The main benefits of this research relate to improving the knowledge that we have on the best
teaching practices for children with learning disabilities. Numeracy and mathematical skills
in general have been shown to be an important component of success in school and are
necessary in almost any vocational environment. But, more importantly, maths skills are
essential in everyday life activities such as cooking and managing personal finances.
Consequently, in any population, independence is partly determined by competence in math
skills. We hope that the results of this study will help professionals working in schools with
children with learning disabilities by providing them with a detailed curriculum that can be
used with children across a wide range of numeracy ability.
Are there any risks involved?
We do not believe that the children participating in the study are being put in risk in any way.
Children in our previous work have very much enjoyed the maths teaching. Your child’s
identity will be protected at all times and the completed study will not include their name, the
name of the school, or any other identifying information.
Your participation is completely voluntary and you reserve the right to withdraw your child
from the study at any time without giving any explanations and without this affecting his/her
education in any way (unless you ask to stop the Maths Recovery teaching with your child).
If you have any further queries about the study please do not hesitate to contact us. Our
details are below. Pagona would be happy to meet you at Ysgol y Gogarth to discuss any
questions you might have.
Pagona Tzanakaki
Appendices
Postgraduate Research Student
Ysgol y Gogarth
Ffordd Nant y Gamar
Craig y Don
Llandudno
LL30 1YE
Email: [email protected]
Tel: 07901992001
Or, you may contact the supervisors directly:
Dr Carl Hughes /Professor Richard Hastings
School of Psychology
Adeilad Brigantia
Penrallt Road
Gwynedd
LL57 2AS
Email: [email protected] , [email protected]
If you have any complaints about how this study is conducted please address these to:
Professor Oliver Turnbull
Head of School of Psychology
Bangor University
Gwynedd
LL57 2DG
208
Appendices
209
Appendix 7b
Research Consent Form for Parents
Please complete the following and circle as necessary:
13. Have you read the information on the Information sheet?
YES / NO
Have you had an opportunity to ask questions and discuss this study?
YES / NO
Have you received satisfactory answers to all your questions?
YES / NO
14. Do you give consent for your child to participate in the study?
YES / NO
15. Are you aware that you can withdraw your child from the study at any time without
giving a reason for withdrawing?
16. Would you like a copy of this consent form?
YES / NO
YES / NO
17. Would you like to be sent a copy of the study or, if it is published, a copy of the
printed article?
YES / NO
Signature______________________________________________________________
Date__________________________________________________________________
Your name ____________________________________________________________
Your child’s name ______________________________________________________
Address_______________________________________________________________
______________________________________________________________________
____________________________Postcode__________________________________
Please return this form, at your earliest convenience, to Pagona Tzanakaki at Ysgol y Gogarth.
Appendices
210
Appendix 8
Letter to parents asking for permission for a follow-up test
8a. Information letter
8b. Consent form
Appendices
211
Appendix 8a
Information letter
Dear parents
During the previous school year (2010-11) we conducted a study on the use of a Mathematics
curriculum called Maths Recovery with young children with learning disability. Maths
Recovery had been shown to help typically developing children who have difficulties in
maths and our purpose was to investigate whether it could be effective with children with
special educational needs as well.
To be able to measure the progress of the children we tested them with some standardized
numeracy tests at the beginning and the end of the teaching period. As you probably
remember, we asked your permission last year to conduct the tests with your child.
The results we have so far are encouraging and suggest that Maths Recovery helps children
with learning disability make good progress in their numeracy skills. However, especially as
there have been no previous studies on Maths Recovery and children with special educational
needs, we would like to see if the improvements we saw have been maintained over time. So
we are asking for your permission to repeat one of the tests that your child has previously
done. Depending on the child’s ability level, testing time will be between 15 and 40 minutes.
It will take place at Ysgol y Gogarth during normal school hours.
Thank you
Pagona Tzanakaki
Postgraduate research student
Ysgol y Gogarth
Ffordd Nant y Gamar
Craig y Don
Llandudno
LL30 1YE
Tel.: 07901992001
Appendices
E-mail: [email protected]
212
Appendices
213
Appendix 8b
Consent Form
Please complete the following and circle as necessary:
Do you give consent for your child to be tested?
YES/NO
Signature______________________________________________________________
Date__________________________________________________________________
Your name ____________________________________________________________
Your child’s name ______________________________________________________
Address_______________________________________________________________
______________________________________________________________________
____________________________Postcode__________________________________
Appendices
214
Appendix 9
Randomization protocol
Appendices
215
Appendices
216
Appendices
217